In music notation, fine (pronounced "FEE-nay") is written above the staff and indicates the end of a repeated section. The word simply means "end" in Italian. It is used in conjunction with the da capo or dal segno notation when the composer doesn't want to repeat all the way to the end, only to partway through the piece.
When used with a da capo al fine marking, it looks like this (complete with staff, time signature, and a quarter note scale):
/\ fine
---| /----------------------------|---------------------|
|/ | | |
---/------------------------------|---|----|------------|
/| 4 | | | | * |
-/-|/\--------------------|----|--|---|----|---*---|----|
| | | 4 | | | | | * | | |
|--|--|--------|-----|----|----|--|--*--------|----|----|
\ | | | | | * | | | |
--\|_/---------|-----|---*--------|-----------|---------|
| | *
\| -*--
/\ D.C. al fine
---| /----------------------------|---------------------||
|/ | | ||
---/------------*--------------|--|---|-----------------||
/| | * | | | | ||
-/-|/\---------|----|-----*----|--|---|---|----|--------||
| | | | | | * | | | | | ||
|--|--|--------|----|----|--------|--*----|----|---|----||
\ | | | | | * | | ||
--\|_/-------------------|--------|-----------*----|----||
| *
\|