In order to fully comprehend the DCT will do a basic study of the Fourier theory and the Fourier transform first.
Whilst the DCT is ultimately used in multimedia compression it is easier to perhaps comprehend how such compression methods work by studying Fourier theory, from which the DCT is actually derived.
The tool which converts a spatial (real space) description of an image into one in terms of its frequency components is called the Fourier transform
The new version is usually referred to as the Fourier space description of the image.
The corresponding inverse transformation which turns a Fourier space description back into a real space one is called the inverse Fourier transform.