It's the Graphics memory. Sometimes, graphics cards are announced as say a Mobility Radeon 9600 64MB, which has obviously, 64MB of memory.
In games, all the walls, the characters and generally, the environment have a "texture" and colour. Such as the grass is green and is generally smooth along the single stick of grass or a rough hewn stone wall is, rough and brown. These all have an image file associated with them, such as a picture of a certain section of the wall, which is repeated again and again across the wall. The larger the picture of the wall, the less repetition there is, thus, the better looking and the more realistic it is. This picture or texture as it is called is stretched onto the wire frame of the wall like putting wallpaper on your wall and the graphics card handles the 'stretching' so that it looks realistic instead of being stretched disproportionately. The graphics card has to constantly draw on the picture, requiring much faster ram to store the 'textures' in. Typically, the ram on a video card, or VRAM is twice as fast as system ram. Video card memory is progressing onto DDRIII and is running at up to 1.1GHz DDR or 550MHz while system memory is only running at around 550MHz DDR or 275MHz. If the textures are too large to fit in the VRAM, then it is compressed, which makes it lose some of it's original quality and decompressing it makes accessing the textures somewhat slower.
And after all that rambling on, the answer to your question: The VRAM is a physical memory chip(s) on your graphics card. VRAM hasnt been upgradable since the old 3DFX days so, no, you cant upgrade the amount of VRAM you have.