Definition and background:
Leaning note; grace note; note of embellishment usually one step above (sometimes, though seldom, it is one step below) the main note. Before an even or unaltered note, the appoggiatura generally receives its face value, that is one-half the value of the note that follows; before a dotted note it receives more than its face value, that is to say that it should be given two-thirds of the value of the following note. If the note is of the same pitch as the principal note of the appoggiatura, the grace note receives the entire value of its principal note, but is carried to the next note with strong portamento.See also non-harmonic note. a musical ornament written just before or after the main note, which takes attention away from the main note and halves its time. it may be written using an auxiliary note in small type, or it may be unwritten and inserted by the performer according to the conventions of the the period. chiefly an 18th-century practice The first half of the principal note's duration has the pitch of the grace note (the first two-thirds if the principal note is a dotted note).
For more information on the music term "Appoggiatura" check out these other resources:
Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary