The amount of memory a video card has onboard.
On GPUReview.com card pages, the framebuffer refers to the amount of local memory on a video card. In the case of reference cards, the amount of memory on the reference card itself is listed, though other variations of the card may have different amounts of memory.
In general, the size of a framebuffer determines the number and resolutions of textures that can be used smoothly in a video game. Typically video cards become limited by the speed of their memory, or the GPU long before they are limited by the size of the framebuffer, but more memory rarely hurts.
Over time, as new games are released that demand more and more memory, video cards with larger framebuffers will show higher performance than identical cards with smaller framebuffers. However, when choosing a card, the speed of the memory should be weighted much more heavily as it more directly affects overall performance.
On GPUReview.com card pages we list all the framebuffer sizes we've found in retail cards, and if there is more than one, we bold the framebuffer size that's considered 'standard' for that card. This is mostly for reference, but if you see a card with 128 MB bolded, but a 512 MB version available, chances are the 512 MB versions are a waist of time and the card only really needs 128 MB to realize its full potential.
Remember that video card companies love to strap 512 MB of slow, inexpensive RAM to a cheap card to make it look more appealing, when in actuality the 512 MB of RAM makes absolutely no difference and a card with less memory and a faster memory clock will give better performance.