A buffer inside a digital camera is RAM storage which temporarily queues images before they're written out to the storage card to speed up the 'time between shots' and ability for the camera to shoot burst (continuous) shots. The very first digital cameras didn't have any buffer, this meant that after you to took the shot you HAD to wait for the image to be written out to the storage card.

Most modern digital cameras (especially those at the prosumer level) often have relatively large buffers which allow them to operate as quickly as a compact film camera while writing data out to the storage card in the background (without interrupting your ability to shoot).

The exact location of the buffer within the cameras system affects the cameras ability to buffer images. While we can't be exactly sure (as no manufacturers have ever made this information publicly available) it's fairly easy to surmise that their are two different types of buffers:

After Image Processing Buffer

With this method the images are processed and turned into their final output format before they're placed in the buffer, this means that the number of shots which can be taken in a burst is affected by the image mode (final file size), using JPEG and/or higher compression and/or lower resolution in cameras like this will increase the number of images buffered.

Examples of cameras which use buffers like this: Canon G1, Nikon Coolpix 990, Canon EOS-D30

Before Image Processing Buffer

In this method no image processing is carried out and the RAW data from the CCD is placed immediately in the buffer, in parallel to other camera tasks the RAW images are processed and written out to the storage card. The problem with this method is that you're always limited to the number of frames you can shoot, no matter what image quality / size you select.

Examples of cameras which use buffers like this: Fujifilm S1 Pro, Fujifilm 4900Z, Olympus C-3030Z