Dedicated VRAM = RAM chips onboard the graphics card. Uses faster RAM than System RAM (the RAM that comes with the computer) and its own RAM controller.
Shared VRAM = The graphics card grabs a section of System RAM (the general RAM that comes with the machine) to use. Is slower, both because the RAM speed itself is slower, and because it has to split access time with the CPU.
Why is dadicated RAM physically faster than System RAM? There are several different RAM technologies, and a RAM design trades off between speed, chip size, heat production, and cost. Dedicated VRAM is optimized for speed, System RAM tends to be optimized to pack the most memory onto the smallest physical chip. Which basically means the VRAM is faster because it uses a larger chip to store less data.