In the Nahuatl language tlàtoāni was the word for 'king' or 'ruler'. It literally means 'speaker' or 'he who speaks well'. It was the Nahuatl term for the leader of an altepetl, a pre-Hispanic city-state, although it carried over to be used by all rulers of the Aztec Empire. The tlàtoāni was the head of the government and the army, and was also the high priest. They were elected by members of the royal house or other leaders, who naturally chose one of their own.
Tlàtoāni is a shortening of an even older term, cuāuhtlahto, meaning 'the speaker and eagle'. If you want to get fancy, the correct pronunciation is /tɬaʔtoˈaːni/. The plural is tlàtòquê or tlahtohqueh (/tɬaʔ.ˈtoʔ.keʔ/). A female ruler was called a cihuātlàtoāni (/si.waː.tɬaʔ.to.ˈaː.ni/). The territory ruled by a tlàtoāni is called a tlahtohcāyōtl. You may also see the terms huēyi tlahtoāni or huey tlatoani, particularly in Spanish; huey means 'big' or 'grand'.
Table adapted from Wikipedia de España: Huey Tlatoani Mexicas