The number of bits wide (and the organization) of the memory bus that connects your GPU to your video card RAM.
Does It Matter?
Yes, definitely. Memory bus width is a huge part of memory bandwidth. And memory bandwidth has a major impact on performance. Especially at the low end, video card manufacturers tend to cut down memory bus widths so they can use cheaper memory, so you always want to make sure you know what memory bus you're actually getting.
In order to process 3D data as much as possible your video card has onboard RAM which typically operates much faster than your system RAM. This onboard video card RAM is connected to the GPU via the memory bus. This connection can be of varying widths depending on what GPU you have. Some GPUs support wider busses than others. Also, most cards support using memory over a smaller bus than the maximum supported by the card.
As a result, video card manufacturers often use cheaper memory with a lower buswidth than the maximum supported by the GPU. This is how you get 4 different versions of a video card with different memory buswidths. Since the buswidth is not heavily advertised (despite its importance), it's very easy to end up with a lower performing card than expected. So be careful.
On the card pages we first display the type of memory bus, and then the overall size in parentheses. The 'type' of bus refers to how the bus is broken up internally to better handle smaller chunks of data. For example the 7600 GT has a 64x2 memory bus, meaning it can process one 128bit chunk per clock, or two 64bit chunks. This segmenting makes the fetching of smaller chunks of data much more efficient since otherwise an entire clock cycle would be taken for a 64bit chunk