Memory (VRAM, video memory) Is a supporting spec, first thing you have to know. Having alot of memory means squat shit if the GPU (the graphics card) itself is underwhelming.
Memory is used to store textures, frame buffers, geometrical data, the works. The amount it can store is finite, based upon the capacity of the onboard video memory. When it runs out, it has to stop, remove data, load new data onto memory. This can cause stuttering, frame drops, performance problems in general, when this happens alot it can be very noticeable. It is referred to as a memory bottleneck. Having more memory means it can hold more data and this obviously leads to fewer stop/reload cycles.
You read me? =]