Wordorigins.org

The state of Illinois is a French version of the name of an Algonquin Indian tribe, the Inini, or “accomplished men.” The French altered the name to Illini and added the -ois suffix to refer to the tribe. The name is akin to the Miami alänia and the Shawnee hilenawe, meaning man or person.

(Sources: Illustrated Dictionary of Place Names; Webster’s Third New International Dictionary)