The symbol is of Etruscan origin and came to us via Roman Republican times as a symbol for political authority, they were insignia of power. The early 'practical use' is to be found within its components which were used for corporal punishments: beatings with the rods and beheadings with the axe. These punishments were the prerogative of the magistrates to apply to unruly citizens, but the magistrates power was to an extent bound by law.
In Rome men holding political office were accompanied by lictores people carrying these fasces around. The more lictores one displayed the more imperium the office holder had.
The lictor's tasks are described as:
The lictor's main task was to attend as bodyguards to magistrates who held imperium. They carried rods decorated with fasces and, outside the pomerium, with axes that symbolized the power to carry out capital punishment. Dictatorial lictors had axes even within the pomerium. They followed the magistrate wherever he went, including the Forum, his house, temples, and the baths. Lictors were organized in an ordered line before him, with the primus lictor (the principal lictor) directly in front of him, waiting for orders. If there was a crowd, the lictors opened the way and kept their master safe, pushing all aside except for Roman matrons, who were accorded special honor. They also had to stand beside the magistrate whenever he addressed the crowd. Magistrates could only dispense with their lictors if they were visiting a free city or addressing a higher status magistrate. Lictors also had legal and penal duties; they could, at their master's command, arrest Roman citizens and punish them. A Vestal Virgin was accorded a lictor when her presence was required at a public ceremony.
As we can see, the sticks are bound together by a leather strap. One reduced modern view is that this merely 'presents unity', as any individual stick might be broken easily, while the bundle would be tough to break. A more detailed discussion for modern readings and the possible symbolic interpretations together with origin discussions is in:
— Adam Cedro: "Fasces. Norwid's intuitions in reading a symbol", Materials Studia NorWidiana 35:2017. doi
But in the earlier Roman times the lictores not only marched before any magistrate. They also sometimes had to make some room for the politician, by using these individual sticks as clubs, if not harsher treatments:
We may take our start from the basic fact that the fasces were not merely decorative or symbolic devices carried before magistrates in a parade of idle formalism. Rather, they constituted a portable kit for flogging and decapitation. Since they were so brutally functional, they not only served as ceremonial symbols of office but also carried the potential of violent repression and execution. If these emblems of office paraded before Roman eyes retained their practical function in the infliction of severe corporal punishment, then despite the advent of provocatio their punitive associations never became as historically "distanced" for the average citizen as have those of ceremonial maces and swords in modern societies. Even after provocatio had been won to shield citizens from their summary use, mass executions of deserters or prisoners of war involving virgae and secures could still be viewed on occasion in the forum. Roman society was therefore unusual in that its central magisterial regalia remained directly functional; the fasces continued as both and instrument of executive power. Thus powerful emotions of pride and fear could focus on them, and their symbolic political significance was accordingly intensified by their aura of latent violence.
— Anthony J. Marshall: "Symbols and Showmanship in Roman Public Life: The Fasces", Phoenix, Vol. 38, No. 2 (Summer, 1984), pp. 120–141 jstor
Also confer to Livius.org: Lictors.
This is also visible in the naming of related instruments:
Fasces were bundles of rectangular or rounded rods that served to distinguish important Roman magistrates and priests. Each fasces was carried by an attendant called a lictor. […]
The fasces thus were insignia imperii and dignitatis (Cic. Q Fr. 1.1.13), and demonstrated the magistrate’s authority to summon and arrest citizens. […] Illegal or scandalous behavior led to the breaking of a magistrate’s fasces following conviction or resignation. […]
At some time during the Early Republic, the ax was removed when the consul was in Rome as a sign of the right of provocatio that allowed a citizen to appeal to the people against a magistrate’s coercion, but outside the pomerium, the axe was replaced in the fasces, indicating of the consul’s absolute military authority (Cic. Rep. 2.31 and 55). […]
Some municipal magistrates also were honored with bundles of rods (usually two), although without the axe, and perhaps called bacilli (Cic. Leg. agr. 2.93).
— Shelley C. Stone: "Fasces", The Encyclopedia of Ancient History, First Edition. Edited by Roger S. Bagnall, Kai Brodersen, Craige B. Champion, Andrew Erskine, & Sabine R. Huebner, print page 2640. 2013.
Bacillum is of course in this context:
Diminutive of baculum (“staff, walking stick”).
bacillum n (genitive bacillī); second declension
A small staff or wand.
The shaft or handle of a tool or weapon.
Or in other words: the supposedly original usage of these individual rods as crops.
For a comparison from different languages Wikipedia entries:
Since we know that the modern appreciation of this symbol for 'republican' purposes is tied to the French Revolution and the American Republic, it is noteworthy that the ancient writers which were used for the inspiration of this symbolism expressed their own awareness of a certain duality that originates from (this) 'power':
The Roman regalia, with their Etruscan origins, were alien to the Hellenistic world, a factor which may well have intensified this symbolism. Worse still, decapitation was seen as brutal and barbaric by the Greeks.
The Latin poets, dutifully hyperbolic, go further in their symbolic use of the fasces for extravagant predictions of conquest, although prose authors also feel the attraction of this symbol. Here the fasces draw the emotions nowadays associated with the flag of an international power, with the added tension of repressive violence. Equally significant is the Romans' own calculation of the effect of their regalia on their subjects as expressed in the pleasurable awareness that they intimidated. This is seen
from the appreciable number of texts which associate the fasces with fear or sheer terror as the antipated response.
Words such as timeo, terror, terribilis, terreo, metus, and vereor are employed in this context, and here again this association of vocabulary may indirectly reveal the users' own
primary response. The pragmatic Romans were surely aware of the
potential of their regalia to cow and impress, and it seems likely that they traded on the fearful glamour of their magisterial emblems to enforce obedience. If so, Roman provincial administration involved more than edicts and routine efficiency, and the panache of their formidable regalia will have provided a large element in the Roman "presence" and an intangible control-technique.
— Marshall, 1984
Going forward from the oldest archeological find of a fasces, an Etruscan version made of iron and found 1897 in Vetulonia — just as Roman author Silius Italicus reports fasces to originate from this very spot — we see this configuration:
From this depiction — albeit with an at least stylised double-axe — we might conclude that already when the Romans took over this symbol, any practical explanation in the direction of 'enhanced stability of a bundle of rods' is no longer discernible.
Before the carnifex took over public executions within Rome, the lictors used the individual elements of the fasces as instruments of chastisement with the rods and execution with the axe. The lictor had to untie the fasces, then undressed (spoliare) and bound the delinquent. When the official then gave the explicit order _"age lege" (enforce the law) did the flagellation (verberatio) take place. In most cases, the actual killing by axe (securi percussio) took place afterwards.
This emphasises that 'the bundle' shows the might and power, in combination of different attributes, but wasn't used as 'one giant strong club'. It was customarily bound probably precisely to not be used 'as is'.