Not sure what camera you have but on my D80 I can choose auto iso or set it myself.
I don't even know if going in auto mode would do an auto iso as I haven't used auto for a long time. I know I can choose iso settings in aperture/shutter priority and when in manual. I think it can also be changed in the P mode.
If you go to higher iso, you can get smaller apertures and/or faster shutter speeds which is pretty much the same as film. You choose higher iso films to get that smaller aperture or faster shutter speed.
The other result is a higher noise level,(as in film grain). The amount of noise varies from camera to camera and make to make. Until the introduction of the D300, I think Canon had Nikon beat for lack of noise at high iso but the D300 is as good or better than anything out there from what I've read.