Well, this is a bit difficult to answer.
Let me start from the beginning.
There are integrated and discrete graphics cards. What that means is that, integrated graphics cards are specific parts of your processor, or CPU, that are dedicated for graphics processing. Discrete graphics cards are separate processors entirely, in a manner of speaking.
An apt analogy is if you have a car engine, integrated graphics would be like one cylinder of your engine being used to say, power the audio. Discrete graphics would be like having a second engine that is solely used for powering the audio.
Anyway, integrated graphics share RAM with other CPU processes. This is because as part of the CPU, they do not have their own allocation of RAM. Generally, they have a set quantity of RAM they are allowed to use--not surprisingly, this takes away from your total RAM. However, as a marketing trick, manufacturers will often display the set quantity of RAM that the integrated graphics can use as its memory. This is misleading. It has no additional memory.
Discrete graphics processors are different in that they have their own RAM. This RAM is specifically for graphics use, and generally has a higher throughput and speed than ordinary RAM. This means that for a discrete graphics card, however much memory it has is separate to the total RAM in your computer.
For more specific details, look up the graphics processor in question to see if it is integrated or discrete, and how much memory it has.
Hope it helps!
Edit:
I want to add that integrated graphics are not necessarily bad. It really depends on what you are looking to do. Gaming on any laptop is something of a joke in terms of cost efficiency, but most "gaming laptops" nowadays do have several GB of graphics memory. Memory, however, is not the most important component of performance. You really want to look at home many processing cores a graphics processor has, and their clock speed. To put it another way, look it up at http://www.notebookcheck.net/Comparison-of-Laptop-Graphics-Cards.130.0.html if you want all the details.