This is a huge topic, but I'll give you the reader's digest version.
RAID (Redundant Array of Inexpensive Disks) is a data storage method used to increase data rendundancy and/or access speed, essentially it allows you to access data more quickly, and/or implement data redundancy (backup). Here's a quick overview of popular schemes:
RAID 0 (Striping): One file is stored half on one disk, half on the second, so that both disks can be accessed simultaneously during read. Most desktop users wont see the performance increase from this. (All RAID schemes are mostly found in a server environment)
RAID 1 (Mirrored): One file is stored in its entirety on both disks, this way if one disk fails, you still have a working copy of the file on the other disk.
RAID 5: RAID 5 combines both aspects of RAID 1 and RAID 0 with striping and mirroring, via parity data (RAID 5 requires a minimum of 3 disks, and the usable storage space is equal to (n-1)*s, where n is the number of disks, s is the smallest disk in the array.) There's plenty of sites that really describe the details of all these schemes. So I wont recreate the wheel here, just google it.
JBOD is a term that's often thrown in with RAID. Just a Bunch Of Disks (JBOD) essentially creates one large drive consisting of many smaller drives. As with all RAID schemes this is transparent to the user.
Like I mentioned earlier, most people won't notice the benifit of RAID (Especially RAID 0) in a desktop environment. These were all developed as server technologies, to increase data security (redundancy) and access time (striping).