The lydian mode is built from the fourth degree of a major scale.
It works well over major7 chords, and was often used by Frank Zappa, and occasionally by Trey Anastasio and Jerry Garcia.

Example:
C major scale: C D E F G A B C
F lydian mode: F G A B C D E F

Fmajor scale (for comparison to F lydian):
F G A Bb C D E F

What's in it:

The mixolydian mode is just like a major scale, except with #4 degree (B natural instead of Bb in the example above).

Listen to the F lydian mode
Listen to an F major scale (ionian)