The frame buffer is what a video card uses to store the images it renders, while it is rendering them.
When it is done rendering, it sends the completed frame to your monitor and starts building the next frame. The amount of frame buffer memory a video board has directly impacts which resolutions it can support-- the more memory you've got the higher resolutions your board will support and at higher bit depths.
The frame buffer usually stores 2 frames: one is being calculated by the 3D accelerator while the other one is being sent to the monitor. This is called double buffering and delivers smoother animation. For 640x480 resolution with 16 bits color this requires 640x480x16x2 = 9830400 bits of memory or about 1.2 Mb of Frame Buffer memory.