The Discrete Cosine Transform is performed at the Block layer.
For MPEG-2 (ISO/IEC 13818-2), it's specified in the Annex A to the Recommendation.
The input of the DCT and the output of the inverse transform (IDCT) are 8x8 matrices of 9 bits/element, while the DCT coefficients are represented in 12 bits (-2048:+2047).
DCT is used to remove the spatial correlation existing among adjacent pixels in order to allow a more efficient entropy coding.
As DCT is performed to the 8x8 block, only the correlation inside the block can be removed. Besides, the subdivision of the image in 8x8 blocks for the DCT process is the cause of the typical block artifacts of all the DCT based compression algorithms.
If DCT and IDCT processes were performed with infinite precisions, they would be lossless; unfortunatly they are performed with limited integer precision so that, even without quantisation, they can produce some impairment.
The DCT coefficients have a relationship with spatial frequencies and, given that the different components have different subjective importance, DCT gives an important tool to remove also the subjective redundancy.
The first coefficient (0,0) is related to DC component, the coefficients of the first line are related to purely horizontal spatial frequencies, while those of the first column to purely vertical ones, the other coefficients are related to diagonal components.
A representation of DCT coefficients
The image on the left side is the original one, it has been divided in blocks of 8x8 elements for the DCT; the image on the right consists of 8x8 images, each of them represents a coefficient of the DCT and consists of the values that such coefficient takes in all the blocks the DCT has been performed to.
The relevance of the DC values and of the low frequencies values can be noted.

As MPEG-1 and MPEG-2 adopt hybrid DCT compression algorithm, DCT may be applied not only to sample-values (Intra blocks), but also to prediction error values (Non-Intra blocks). For the latter the DC coeffients are no more so important as for the former, but their relevance is quite similar to the other low frequencies coefficients'.