This Wikipedia article should explain all you need, but it gets pretty advanced. Here are the basics that you'd probably be interested in.
http://en.wikipedia.org/wiki/RAID
First, most RAID is redundant. RAID was designed to be redundant. The idea, basically, is that you mirror the same data over more than one hard drive, so if one fails you lose no data.
However, there are speed benefits as well. By having twice as many readers over the same data, the hard drive performs faster than a single hard drive. The disadvantage for redundant RAID is that, for example, if you put in two 100GB hard drives, you only get 100GB of storage.
The other kind is RAID 0. It came after the original types of RAID, and is just used to increase performance. It ties two hard drives together (two 100GB hard drives gives you 200GB of storage), and the additional read head makes it that much faster. However, it isn't redundant. If a drive fails, you're SOL.
The two basic RAID levels are 0 and 1. 0 is non-redundant, 1 is redundant. Most entry-level RAID controllers will only support these levels. 2 through 5 are more advanced. They simply differ in exactly how they mirror the data over multiple drives, with varying advantages to each.
EDIT: To make it clear, I over-simplified a lot. This is just intended as a primer for the basics; don't take it as holy writ.