In reference to instrumental (and probably vocal) music:
Anything that's not Popular and not Jazz. Generally refers to anything that's twentieth century (but not jazz). or earlier (including classical, romantic, baroque, etc.) some more exotic historical music (such as African drumming, for example) would probably not be considered legit, although those works of Bach, Beethoven, and Chopin would be. After hearing the use of the word more and more you come up with a clear sense of what belongs to the category and what does not. Until then keep listening.
Also sometimes used to describe equipment. Once when I went into my local music store and asked for a tenor saxophone mouthpiece, I was asked "Jazz or Legit?" This was my introduction to the term. Thankfully the person who asked the question, although somewhat of a local jazz personality, was forgiving.