A Double Sharp raises the note by Two Half-Steps. A Double Flat lowers the note by Two Half-Steps.
The last two accidentals are the Double Sharp and the Double Flat. While these two types of accidentals are not as common as the sharp, flat or natural they are a necessary part of the musical language.
A double sharp raises a note by two half-steps. A double flat lowers the note by two half-steps.
If the note already has a sharp and needs to be raised by one half-step it will be a double sharp. If the note already has a flat and needs to be lowered one half-step it will be a double flat.