basically there are two types of video controllers:
Integrated (IGP): the video controller is part of the chipset (or even the CPU). Video memory is shared with the system memory. For some IGPs, a separate memory chip can be installed (for example AMD's sideport memory) by the system integrator (not by the user!).
"Dedicated video": There is a separate video chip installed, that also has its own memory. For higher demand, extra memory can be taken from the system memory.
What is better? Well, the answer depends on the personal needs and usage scenarios. For office/internet usage, the IGP is sufficient. Plus there is better battery life and less heat.