RAID stands for
Redundant
Array of
Inexpensive
Disks (believe it or not) - it's main purpose is to allow you to turn several small disks into one large partition (generally known as a RAID 0 partition). However, there are different types of RAID which also give redundancy options - RAID 1 is basically where one disk is mirrored on to another one - this happens automatically and the write occurs on both disks at the same time ensuring you always have a complete copy of your information. Other types of RAID exist for systems with more than two hard disks, RAID 5 being the most common which allows for one disk to fail without losing access to your data. Certain RAID types also bring performance benefits as well, but that's not really too crucial for the home market.
Don't make the mistake of thinking of RAID as a backup - it's not. It's fault tolerance. In a RAID 1 with two disks, one of those disks can fail and you won't lose access to your data. As long as you replace the faulty disk, the RAID will then automatically rebuild itself and once done, you're protected again. The reason this isn't a backup is because it literally only protects from hardware failure. If you delete a file accidentally, it's deleted on both disks immediately - there's no way of getting the file back (without resorting to recovery tools etc.). Same goes for corruption - a corrupted file is corrupted on both disks immediately.
For that reason, you should use RAID to protect your data from hardware failure, but you should still keep a regular backup to protect from other mishaps.
BTW - I can recommend the Synology NAS devices - I've had one for a few weeks now and am very taken with it