Google definition:
RAID (originally redundant array of inexpensive disks; now commonly redundant array of independent disks) is a data storage virtualsation technology that combines multiple disk drive components into a single logical unit for the purposes of data redundancy or performance improvement.
There are a number of common RAID array configurations:
RAID 0:
This is also known as "striping" or a stripe of disks. Data is distributed (or "striped") across a number of drives, without any copy of the data, or any parity information about the data.
Disks: Minimum 2 disks required. Disks are striped, no mirror, no parity
Good for: performance - it is very quick to read and write to
Bad for: redundancy - if a disk fails, you've lost your entire RAID array. No good for critical systems
RAID 1:
This is also known as "mirroring" or a mirror of disks. The same data is written to two disks. Should one disk fail, you still have a complete copy of the entire disk on the other mirrored disk.
Disks: Minimum 2 disks required. Disks are mirrored, no stripe, no parity
Good for: redundancy - if a disk fails, you still have a copy of the entire disk.
Bad for: useable disk space - 2 x 1TB disk drives configured as RAID 1 only gives you 1TB of useable disk space
RAID 5:
This is the best cost effective option for both performance and redundancy
Disks: Minimum 3 disks required. Disks are striped, with distributed parity
Good for: Read performance due to striped disks. Also good for redundancy - if a disk fails, the data can be recovered based on the parity information
Bad for: write speeds can be slow
RAID 10:
Also known as RAID 1 + 0, or a "stripe of mirrors", it combines both RAID 1 and RAID 0.
Disks: Minimum 4 disks required. Disks are striped, and mirrored
Good for: Performance due to striped disks. Good for redundancy due to mirrored disks. The best option for critical systems (especially databases)
Bad for: cost - the most expensive option
Resources:
PCWorld post on RAID:
http://www.pcworld.com/article/194360/raid-made-easy.html
The Geek Stuff:
http://www.thegeekstuff.com/2010/08/raid-levels-tutorial/
There are some additional less common RAID levels (2,3,4,6), details about these here:
http://www.thegeekstuff.com/2011/11/raid2-raid3-raid4-raid6/