What was a "Teuctli" in Mesoamerican history? I do not know how to spell it. I know that was some kind of leader.
From what I have read, several bands of Chichimecs came into the Valley of Mexico and took over various city states. Each tribe and city state was ruled by a Tlatoani. The Acolhua tribe took over the city of Texcoco. Xolotl of the Acolhua tribe was the commander of the invading Chichimecs and used the title of Chichimeca Teuctli or "Lord of (all the) Chichimecs" as well as being the first Tlatoani of Texcoco.
The descendants of Xolotl continued to claim the over lordship of the other Chichimec realms in the Valley of Mexico.
The Tepanec tribe ruled the city of Azcapotzalco. Tezozomoc became the Tlatoani of Azcapotzaloc in 1353, 1367,or 1370. Tezozomoc eventually claimed the title of Chichimeca Teuctli and the over lordship of the Valley of Mexico.
Tzozomoc fought Ixtlilxochitl I (reigned 1409-1418) Tlatoani of Texcoco, defeating him in 1418. Ixtilxochitl as killed while his son Nezahualcoyotl (1402-1472) hid in the branches of a tree and watched.
Tezozomoc became Totoquihuaztli and died in 1426, allegedly aged 106. His son Maxtla as defeated in 1428 by Nezahualcoyotl Tlatoani of Texcocco, Itzcoatl Tlatoani of Tenochtitlan, and Totoquihuaztli, Tlatoani of the Tepanec city of Tlacopan.
They formed the Triple Alliance in 1428 to conqueror and rule as much land as they could. Nezahualcoyotl retook the title of Chichimeca Teuctli, Totoquihuaztli took the title of Tepanaca Teuctli ("Lord of the Tepanecs"), and Itzcoatl took the title Culhua Teuctli, ("Lord of the Culhua"). Itzcoatl's father's mother was a daughter of a king of Culhuacan, and the rulers of Culhuacan claimed descent from the Toltecs, so Itzcoatl stressed his high descent. Teuctli in those titles more or less meant overlord or high king instead of simple lord.
The Mexica or Azteca of Tenochtitlan expanded their conquests and tribute system much faster than Texcoco or Tlacopan, so eventually their rulers became much more powerful than the other two combined, and it is common to refer to the Aztec Empire.
And that is the version of the meaning of teuctli that I have read.
The name of the office held by Montezuma according to the best accessible information was simply Teuctli which signifies a war chief. As a member of the council of chiefs he was sometimes called Tlatoani which signifies speaker. This office of a general military commander was the highest known to the Aztecs.
The term also had a more general use, which is explained (same source) this way:
The title of Teuctli was added in the manner of a surname to the proper name of the person advanced to this dignity as Chichimeca-Teuctli ,Pil-Teuctli and others The Teuctli took precedency of all others in the senate both in the order of sitting and voting and were permitted to have a servant behind them with a seat which was esteemed a privilege of the highest honor Clavigero U 137
So there were at least two uses for the word. One, when added to a name to indicate the individual deserved the highest respect, and the second, indicating the highest position possible of general military commander.