6 Gb is the RAM for your system. Whenever you run any program, it has to load all of the data required to run it (more or less) successfully into RAM. Reason being is that RAM, while much smaller in size, is definitively faster than hard drives are when it comes to accessing and retrieving data. Think of it as your system's workspace, whereas the hard drive would be the file cabinet that holds everything else that you're saving but not necessarily using at the moment.
VRAM (Video RAM) is essentially the same thing, but dedicated solely to graphical applications (applying textures and shaders, drawing the framebuffer, etc) and only controlled from the GPU itself via directx or opengl drivers. The proximity of the dedicated RAM on the graphics card is crucial to providing the fastest possible response for graphical applications.
FFXIV has a pretty strict requirement of 512 MB VRAM or higher, evidenced by the fact that the benchmark would crash every time until I swapped cards to one that had enough VRAM. It should say somewhere near the model or name of the card how much VRAM it has, i.e.: RADEON HD 5870 1GB DDR5 HDMI Graphics Card HD587XZNFC
(1 Gb VRAM) Edited, Jul 17th 2010 8:45pm by bsphil