In music notation, an appoggiatura is a type of ornamentation represented by a small eighth note preceding and slurred into another note placed a step higher on the staff. It is not counted as a note for the purposes of filling in the time signature for the current measure. It comes from an Italian word meaning "to lean".
Normally, an appoggiatura is played on the beat of the note it precedes and "steals" half its specified duration (e.g., a quarter note becomes two eighth notes). The exception is when the main note is dotted, in which case the appoggiatura takes up two-thirds of its duration (e.g., a dotted quarter note becomes a quarter note and an eighth note).
It looks something like this (complete with staff and time signature:)
/\
---| /-----------------------|------------------|----------
|/ | |
---/------------*----|\------|-------|----------|----------
/| 2 | . | | |\ |
-/-|/\---------|-----\_-*----|---|\--|-----|/---|----------
| | | 4 | | | . | |\ |
|--|--|--------|-------|-----|---\_-* .----|----|----------
\ | | | | * |
--\|_/-----------------|-----|------------------|----------
|
\|