When decoding video it is common that the next macroblock to be decoded will look somewhat like the surrounding macroblocks. H.264 decodes macroblocks in so called ``scan'' order, i.e. do the first row, left to right, then move on to the next row and repeat. Imagine a scene with a large section of sky covering the top half of the frame. A good guess to the content of the next macroblock might be the shade of blue that is directly surrounding it (from the already decoded macroblocks above and to the left). So we guess that the macroblock we're encoding is blue, then code the difference between that and the actual colour values. If our macroblock is close to the prediction, which it usually is, then we don't need to code much at all. This is for the most part how intra coding works. The name comes from the fact that no data outside of the current picture is accessed, as opposed to inter coding that looks at the previous and future frames to help compression.
MBAFF changes which neighbours need to be referenced when predicting the next macroblock. This means that it's not usually just the top and left macroblocks that the pixels for intra prediction come from. The rules for which macroblock to reference are fairly convoluted, but do make sense from a compression point of view. I have several pages of diagrams trying to make sense of it!