I was going to find sources for the Wikipedia article on Thales of Miletus, since the section on divinity has almost none, I was wondering what "divinity" even means in the context of Ancient Greece. Does it mean Arche? Or does it mean the Greek Gods we were taught in school?
Actually, "divinity in the context of Ancient Greece" is a bit broad. There were quite some diverging schools of thought, arguing about just exactly that question. The pre-socratics like Thales in particular had quite some different ideas that just seemed to contradict many aspects of other philosopher's ideas. Seemingly as if they would argue in a pre-dialectic debate of sophists. Fair to say: after Plato things have to be analysed with different eyes.
Narrowing this down to just Thales is fraught with problems, as it is not even entirely clear if he himself wrote down anything at all. (Personally I think it's a fair guess to assume he did.) But more importantly than that we have nothing approaching an original text, the surviving fragments from different authors tend to be read and interpreted with philosophical glasses and and with an inherent tendency of a historians's myths: those of congruence and coherence.
Therefore, let me try and emphasise to apply a healthy dose of salt to the following – before generalising this to all of "divinity in Ancient Greece" and even just Thales. This is not to say that a pure relativism should be preferred for each fragment. It is just a reminder that in the history of ideas there is very probably way too much stringency interpreted into the texts later.
Answering the question on Thales, arché and Greek Gods directly: the homeric works and Hesiod's theogeny present "the Greek Gods as told in courses" about Greek mythology and the first known cosmogenies (e.g. Theog. 116–133). In contrast to mythological cosmogeny there are the first philosophiocal cosmogenies: Thales commonly marks the great departure from this anthropomorphic worldview with an idealistic reduction of natural principles to really first causes and/or first movers. His views might be summarised in very short terms as "all whatness is wetness." (In the sense of coming from water, not still being water.)
The ancient sources disagree as to whether T. recorded his theories in writing. Those who argue for it name the titles of three works: Ναυτικὴ ἀστρολογία (Nautikḕ astrología, 'Nautical Astronomy', in hexameters), Περὶ τροπῆς (Perì tropês, 'On the Solstice') and Περὶ ἰσημερίας (Perì isēmerías, 'On the Equinox'; Diog. Laert. 1,23 = 11 A 1 DK). The main source for the philosophy of Thales is Aristotle (Aristoteles 4), although he is calling on secondary sources (probably doxographical compendia of Hippias of Elis.
According to Aristotle, T. was the founder (archegos) of natural philosophy, being the first to postulate a material principle (ἀρχή/archḗ) for 'all things that are' (ἅπαντα τὰ ὄντα/hápanta tà ónta) and to break with the tradition of divine genealogies (Aristot. Metaph. 1,3,983b 17-984a 3). For T. the principle of 'all things that are' was 'water' (ὕδωρ/hýdôr). It is not clear whether this should be taken as the weaker claim that 'all things that are' have come from water, or the stronger, that 'all things that are' consist of water. Aristotle supposes that T.'s theory was inspired by the observation that all life comes from moisture. T. was said to be the first to explain that the Earth is at rest because it floats on water, which was based on his observation that solid objects like wood could float on water but not on air (Aristot. Cael. 2,13,294a 28-b 1 = 11 A 14 DK). T. declared magnets to be ensouled because they move iron. From this, Aristotle correctly deduced that T. understood the 'soul' (ψυχή/psychê) as the origin of motion (Aristot. An. 1,2,405a 19-21 = 11 A 22 DK). Another statement attributed to T. (πάντα πλήρη θεῶν/pánta plḗrē theôn, 'everything is full of gods', Aristot. An. 1,5,411a 8 = 11 A 22 DK) may be the generalization of the former theory, inasmuch as it refers to the ceaseless motion and change in the cosmos, which must have its origin in immortal souls.
Betegh, Gábor (Budapest), “Thales”, in: Brill’s New Pauly, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry. DOI
When trying to consolidate these fragmentary views with the three first natural philosophers we can combine, contrast and discern some of these principles, including the arché. Thales, Anaximandros and Anaximenes:
Each of them specified a basic stuff or ἀρχή (archḗ), of which all the phenomena of the natural world are modifications only. The three archaí - water, the ‘unlimited (ἄπειρον/ápeiron) and air respectively - could fulfil this role in different ways. Anaximander's extra-cosmic ápeiron apparently controlled the processes of the cosmos by being the source of the original matrix of the world. The two intracosmic principles - water in the case of Thales and air in the case of Anaximenes - could be intimated by the diverse and various forms in which they can be present in other bodies: all the major components of animal and vegetable bodies are permeated by water, whereas air can freely infuse all sorts of porous bodies, and apparently human and animal souls are also constituted by the airy breath (pneúma) of these living beings.
Control, governing and rule are the key concepts of the Milesian philosophers: the archḗ holds every process in the world in its sway. Thus, she is the deity that replaces all the mythical gods. The testimonies about Thales add that the principle is also basic by being able to transform into all the other materials in the world (Aristot. Metaph. 983b 6ff.). Even if one were inclined to doubt this testimony, it is clear that for Anaximander, the key position of the archḗ rests on the processes which bound the principle to the other substances, and these to each other. As the ápeiron is extra-cosmical, it cannot exert any direct rule on the processes of the world (other than containing and holding it together). Hence it can be said that the first two Milesians held an - at least implicit - theory of change. Anaximenes, however, already formulated an explicit - albeit still rudimentary - theory of change, specifying the processes - condensation and rarefaction - which link different stuffs to each other and to air, the archḗ in his philosophy. Hippon and Diogenes of Apollonia in the 5 cent. BC revived the Milesian fundamental teachings about archḗ. The knowledge of the dependency of the universe on a superior deity, the source and governing principle of all things, passed over to the entire Greek philosophy.
Bodnár, István (Budapest), “Milesian School”, in: Brill’s New Pauly, Antiquity volumes edited by: Hubert Cancik and , Helmuth Schneider, English Edition by: Christine F. Salazar, Classical Tradition volumes edited by: Manfred Landfester, English Edition by: Francis G. Gentry. DOI.
To break that down into simple terms, the following may be helpful.
The Greeks were familiar with the idea of the immortal Homeric gods. Anaximander added two distinctive features to the concept of divinity: his apeiron is an impersonal something (or “nature,” the Greek word is φυσις), and it is not only immortal but also unborn. However, perhaps not Anaximander, but Thales should be credited with this new idea. Diogenes Laertius ascribes to Thales the aphorism: “What is the divine? That which has no origin and no end” (DK 11A1(36)).
Dirk L. Couprie: "Heaven and Earth in Ancient Greek Cosmology. From Thales to Heraclides Ponticus", Springer: New York, Dordrecht, 2011, p 91.
That might be put in anachronistically modern terms as a somehow "animistic" world view. A better term which will probably less commonly understandable might be Hylozoism. Everything has a soul, everything is divine and that part of divinity permeates the cosmos and everything in it. Aristotle himself was already puzzling together the supposedly correct meanings in what he read in Thales, with "that the soul was something kinetic since he said that the [lode]stone has soul because it moves iron" (De anima 405a19–21)
Motion observed in everyday life is not a manifestation of mechanistic laws of nature, but an expression of life hidden even in the most lifeless guise. This belief is carried to the extreme in Thales’ statement that "all things are full of gods". In this way, the whole of nature and everything in it is not only alive, but also divinized. And all this began with water.
Adam Drozdek: "Greek Philosophers as Theologians, The divine Arché", Ashgate: Aldershot, Burlington, 2007, p6–7.
"Divinities" may mean gods, personified. For Thales and most following this "school" or line of thought tradition this seems better translated as an abstract "the divinity" or "the divine" principle.
For historians of ancient Greece, the word "divinity" usually denote their gods, deities, and mythological figures. Here's an example from Mark Munn (a historian), a full paragraph to better illustrate (emphasis mine):
Maternal deities are many to name, and even within the comparatively orderly classical Greek pantheon their roles often overlap. Multiplicity and diversity seem to be virtues in this system of conceptualizing divinity, although our own understanding of it tends to grow by emphasizing the separation of roles. Into the classical Greek system made known by Homer and Hesiod, later sources introduced a deity called the Mother of the Gods. Her roles overlap those of other deities in all directions: she is variously described as a devoted mother, a chaste wife, an impassioned lover, and a virgin daughter; in some stories she is even male, or androgynous in origin. She is vulnerable and she is powerful; she attacks and she protects; she drives mad and she makes wise; she dances and she contemplates; she loves the wilderness and she keeps cities. With so many valences, the Mother of the Gods became exceedingly popular in cult, yet at the same time she became almost transparent, and hard to separate from other divinities whose roles she shared.
Source: Munn, M.H., The Mother of the Gods, Athens, and the Tyranny of Asia - A Study of Sovereignty in Ancient Religion (2006), pp. 3-4.
The Greek term "archê", in the context of Presocratics (such as Thales of Miletus), does not normally denote "divinity" because a better approach is to see the Presocratics as natural scientists or "inquirers into nature". Hence this Greek term "archê" refers to a cosmological and materialist perspective of nature/life (e.g. "essence/origins of life").
Finally, in lieu of a detailed discussion on Presocratic philosophy, and what "archê" should denote, have a look at SEP on Presocratic Philosophy.
Mark Munn, in his book and that paragraph, was referring to Kybele (Cybele).