Graduated filters are often used in landscape photography when you want to even out the exposure of a scene. For example, if you are shooting a scene that has some sky and some land. The sky may be a lot brighter than the land so you would have to choose between blowing out the sky or leaving the land in dark shadows.
With a split or grad filter, you would place the dark part over the bright sky, thus bringing it closer to the light levels of the land...and giving you a better exposure for the overall scene.
I don't like the idea of round grad filters, because they force you to place your horizon where they are on the filter...usually in the middle. Square/rectangular grad filters allow you to move them over the lens, placing the split where it fits your composition.
A straight up ND (neutral density) filters is used to eat up some light, so you can do things like getting a longer shutter speed, as mentioned by LarryD.