The Lydian mode is Mode 5 of the church modes used in Gregorian chant. In modern terms, it is most easily described as the scale from F to F using only the white notes of the piano. In order to construct the scale starting on other notes, follow the pattern ascending from tonic: whole step – whole step – whole step – half step – whole step – whole step – half step.
A handout showing the mode starting from all twelve notes is available here.
The Lydian mode is considered a major mode because of the major third above the tonic. It differs from the major scale by having a raised fourth degree, though some chants will use a B-flat negating any difference between this mode and the major scale. The ancient Greek Lydian mode in the diatonic genus resembles the major scale rather than the ecclesiastical Lydian mode.
Some themes in the Lydian mode include: