Image sensors are not perfectly noiseless, of course, and the higher the ISO is, the noisier the image, which appears as random speckles of colored dots.
You don't notice the difference, though, because you're probably shooting in JPEG mode, not in RAW. In JPEG, the Rebel tries very hard to cover up its sins, and will blur away sensor noise, which is hard to notice unless you grovel over areas of fine detail at 400% magnification.
Second time I've linked this in this thread, but http://www.dpreview.com/reviews/nikond5100/page20.asp shows some great examples of what sensor noise looks like over a range of ISO values.
Edit:
Useless editorializing: A SLR isn't a great purchase for someone who knows very little about photography. A point-and-shoot is lighter, cheaper, more durable, easier to use, and in the vast majority of situations, will produce identical results to a SLR. You then graduate to a real camera when get fed up with the various fiddly technical limitations of a point-and-shoot; and bonus, you still have the small camera, which is the one you take with you when climbing mountains, or on vacation, rather than lugging around five kilograms of japanese glass.
Tedious polemic: I dearly hope you have more than one lens. The enormous price premium of a SLR is mostly for the privilege of being able to change lenses. If you just stick with the kit lens, then you will have spent rather a lot of money to accomplish nothing a point-and-shoot couldn't do.