Traditionally IGPs have been separate chips on the motherboard, though most modern systems have it built in. Both the traditional IGP on a chip, and IGP on the same package as the main processor (what AMD calls an APU) use/share ram with the main system - and you can set the amount of ram in the bios. It would be possible to have a discrete processor on board (for example on a laptop), so having its own ram would be one defining feature that seperates a IGP (which shares ram) from a discrete graphics chip. Of course, on a desktop, most systems use a significantly more powerful PCI-E(or AGP if its old enough) card.
Up until recently, IGPs have either been about 2-3 generations behind the current discrete graphics cards - the current intel IGPs are about as good as a low end graphics card - Anandtech compared current laptop IGPs with discrete cards for diablo III and found them wanting
The advantage with IGPs is they are good enough for basic things like casual gaming, may do some things better (the sandy bridge/ivy bridge cards accelerate video transcoding for example), and come with the system. Most modern motherboards will support using it.
Even a mid range, last generation graphics card will crush any IGP for gaming purposes.They should also crush any IGP in the sort of things a graphics card does better than an IGP.
If you have a program that says it has a minimum amount of video memory, get that graphics card, cause ram isn't everything - The increased speed, processor power and cores and everything else will result in a noticeable difference in performance.