A computation that cannot be performed under any practical scenario, either now or in the foreseeable future. Like winning at chess by enumerating every one of the 10120 possible combinations of positions of pieces on the board, or cracking an AES-encrypted message with a sufficiently long key, by trying every possible key. Even if the entire mass of all the known galaxies was converted into Intel Core 2 Duo processors plus sufficient RAM and other associated bits, and put to work on running the computation, it would take them longer than the age of the known Universe to complete the search.

Mathematicians don’t like to call this sort of thing “impossible”; they reserve that term for something that “cannot be done, no matter what”. The mere fact that you can describe a way to perform the computation means that it is, in principle, possible, albeit not very possible.