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     |                                      
----|--|--|---------|--------------------------------------
     \ |  |                                               
------\|_/-------------------------------------------------
       |                                                  
      \|