Basically, it's a magic square that remains magic after all its numbers are raised to a specific (fixed) power. Satanic squares of small dimensions are not possible to build, the first known square is a 8x8 matrix:
This square has a sum of 260. Raising every number to its power of two gives the following square:
Which is a magic square with a sum of 11,180
See also: Magic square, Diabolic square