Discrete Cosine Transform is a variation on the Discrete Fourier Transform. It is used in basically every lossy compression format ever. The reason DCT is preferred is that discrete transforms are cyclic. So the DFT has a jump at the edges of the data, where it wraps around. (this is why windowing is frequently used in DFT) This jump at the edges leads to a fat tail in the frequency spectrum, which does not compress well.