Legible goes back to the Latin word legibilis, meaning "that can be read." If you can read someone's handwriting, it is legible. The person might not have perfect penmanship, but if you decipher the letters, the writing is legible.
What is the root of the word illegible?
Same way Illegible comes from Prefix Il means "not" such as Illegal (not legal) + same Latin word legere as in word eligible means to read or to pick. Il means "not" + Legible means "to read".
What does the word illegible?
: impossible or very hard to read His handwriting is illegible. Other Words from illegible. illegibly \ -blē \ adverb.