In music notation, a double flat is a stylized 'bb' which indicates that a certain note should be lowered by two half steps. It is only used as an accidental, never in the key signature.
A double flat looks something like this, when used as an accidental with a half note:
/\
-------| /-------------------------------------------------
|/ b
-------/----------bb O--------------------------------------
/| |
-----/-|/\--b-------|--------------------------------------
| | | b |
----|--|--|---------|--------------------------------------
\ | |
------\|_/-------------------------------------------------
|
\|