What does "enharmonic" mean?

Enharmonic: (Mus.) (a) Pertaining to a change of notes to the eye, while, as the same keys are used, the instrument can mark no difference to the ear, as the substitution of A for G#. (b) Pertaining to a scale of perfect intonation which recognizes all the notes and intervals that result from the exact tuning of diatonic scales and their transposition into other keys.