A redouble is a call which is made when the last action is a double by the opponents. Its natural meaning is to further increase the score of the contract.
The only correct form, when spoken, is the single word redouble. When bidding on a bidding sheet, the correct form is letters 'XX'. Abbreviations used in literatures include XX, rdbl and redbl.
As a redouble does not take up any bidding space, and the need of redoubling for penalty is rare, it is commonly used for conventions.