RAID stands for Redundant Array of Inexpensive Disks -- or if you'd like, Redundant Array of Independent Disks.
RAID level 0 is really not redundant in any way, so purists will argue that by definition it really isn't RAID. All RAID 0 offers is data striping. This is a process where multiple drives are used to store information, by storing it in a "stripe" of a defined size on each drive. If a file is larger than the stripe, it is then stored on the next drive in the array.
A benefit of this type of setup is that the data transfer is equal to the transfer rate of the slowest drive, multiplied by the total number of drives. A problem with this setup is that if one drive goes bad, all data/files on the entire system, are lost.
RAID 1 is mirroring of one drive onto another. This type of setup is very useful for managing data, especially for things like webservers and database servers. The key benefit of this RAID setup is its redundancy. However, where it lacks is write time to disk. Also, it is an expensive solution because you have to buy at least 2 disks to store the amount of data that could fit on one.
The best of both worlds is RAID 0+1 (also known as RAID 10). It combines striping and mirroring. Typically, this is a 4 drive setup, where either you stripe the mirrors, or mirror the stripes. It offers the advantages of RAID 0, but has the disadvantages of RAID 1.
There is also RAID 3, RAID 4, RAID 5 and RAID 6. Since these are generally not offered on typical controllers (ie, ones that come on your motherboard, or those you get at Best Buy), I won't go into detail on them.
