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