It's when you buy two disk drives and then use hardware or software to make them act like a single disk drive. Different "levels" can be used to increase performance and/or reliability when you do this. A couple of simple examples:
RAID 0 - Improves transfer rates by alternating blocks of data between the two drives. This lets you transfer data up to twice as quickly by directing I/O to both drives in parallel. If you buy two 1TB drives then you use them as if you've got one giant 2TB drive. But you loose ALL your data if EITHER drive dies.
RAID 1 - Every block of data that's written to one drive is also written to the other (also known as "mirroring"). If one drive dies you can still access your data by reading it from the other disk. If you buy two 1TB drives then it looks like you still have a 1TB disk, but the data is actually replicated on two physical drives. Protects against drive failure, but not against other risks such as accidental file deletion, viruses/corruption, etc.