As dullard said, video card memory, and colour depth (the number of bits) have nothing in common.
This is hopefully going to be an OK way to explain video card memory (butchered slightly from my teachings on the CPU, and the internal memory on that)
All (modern) video cards have some memory onboard. This memory is used to store textures, player models, and any data that the graphics card might need in order to do it's job.
The onboard memory on the graphics card will be super quick. This means that it is really fast for the "core" of the card, the bit of it that does all the calculations etc, to access, and therefore makes the graphics card quick.
The amount of RAM on the card, determines how much stuff can be held. Textures in newer games are reaching like 70-80MB
each, so of course it is useful for this to be able to be stored on the graphics card itself.
If the texture is bigger than the memory on the card itself, then it will use your normal system RAM.
Think of accessing the onboard video RAM as like walking to your fridge in the kitchen. From your bedroom (the "core"), it doesn't take long to go backwards and forwards to the fridge, which is just in the next room. Going to main system memory, however, is like walking half a mile to get to the local shops for the same thing.
If you have a fridge that can only hold 5 beers, then if you have to go to the shops often to stock up, but say your fridge holds 20 beers, then you have to go to the shops less often

That's why more video card memory is useful
Hope that helps, and hasn't confused you too much!
Confused