Humans are a visually-oriented species. The most important form of output a computer has is the monitor you're reading this on. But, just as important is the hardware which controls the images that display on that screen.
In the world of laptops, there are always a number of compromises that must be made to try and make it as useful and as portable as possible.
There are two general approaches to handling graphics hardware in computers today. You can have separate, or 'dedicated', hardware that does all the graphics processing for the system, or it can be built (or 'integrated') into the main control components. An integrated solution is much more efficient in terms of space and power requirements, but is much less capable than a specialized system.
Not that long ago, integrated graphics did not even have enough power for fairly routine tasks such as looking at PDF documents. However, that is no longer true, and integrated graphics are perfectly acceptable for anything other than truly graphics-intensive tasks. These include many mainstream games (of course), animation programs, drafting programs, and some high-powered art programs. Unless any of these is a pressing need, it would be best to go with an integrated solution in a notebook.