Double Sharps
A Double Sharp is an accidental used to raise a note by a whole step (two half steps).
Double Flats
A Double Flat is an accidental used to lower a note by a whole step.
To raise a note by a whole step means moving two half steps to the right to the next adjacent key on the piano keyboard. To lower a note by a whole step means moving two half steps to the left to the next adjacent key.
Enharmonic Notes
Remember that the same pitch sound on a piano keyboard can have more than one musical note names.
C double-sharp is a whole step higher than C, which is the D key on the piano keyboard.
E double-flat is a whole step lower than E. It is also the D key on the piano keyboard.
C double-sharp, E double-flat and D are enharmonic equivalent or enharmonic notes. They share the same pitch and sound exactly the same when played on a piano, but they are written differently on the staff.
A piano keyboard showing all the enharmonic notes.
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Piano Music Theory 