RAID is the logical inverse of a partition.
A partition is taking one physical drive and making multiple logical partitions out of it. Logical Volumes or just Volumes is the usual term for the usable spaces created.
RAID is taking multiple physical disks and arranging them into 1 Logical Volume. This can be done in different ways for different benefits. For all of this assume your drives are all af the same size in a set. Most RAID drivers require this.
I get RAID 1 and RAID 0 confused, but one is striping and the other is mirroring.
In mirroring mode you write the same data to multiple disks (usually 2) so that if one drive fails, you still have all of your data fully usable. This is roughly the same speed as just a normal drive, but it keeps your data safe.
In striping, you write some data to one drive, then to another (usually 2) in round robin fashion so that any lengthy read or write involves all drives in the RAID set equally. This makes the max throughput of the RAID set the sum of the throughputs of the drives. The latency is the same as any one of the drives.
You can put RAID 1 over 0 or vice versa. For instance, involve four drives in two groups of two so that you double the throughput, and you get redundancy of 2 copies of everything. 4 30G drives would feel like a double fast 60G drive, and any 1 drive could fail without destroying data.
Raid 4 usually uses lots of drives, but at least 3. (often 5 or more) This uses all but one drive like a striped set, making access fast. The last drive keeps parity for the corresponding bits on all of the other drives in the set. This means that 7 drives act almost as fast as the sum of 6 of those drives and any 1 drive can fail without losing data. If a data drive fails, it's data can be rebuilt by reading known data, and inferring the missing data using the parity disk. Raid 4 is never used, but it's the stepping stone to understanding RAID 5.
Raid 5 fixes a problem where RAID 4, under certain (fairly common) access situations, would act no faster than a single disk. Usually the parity disk would become a bottleneck; so RAID 5 splits the parity job between the disks depending on where the data is being stored. RAID 5 also allows any one disk to fail without loss, and gives performance roughly equal to the sum of the throughputs of all but one drive in the set, just like RAID 4 on a good day. The control for this is tedious though, and doing it in software is so laborious that it is often slower than just using a single drive. Also, it's not as fast at writing as it is at reading, unlike single drives.
What I'd like to see is RAID 5 over 5, where you use 9 drives in 3 groups of 3, with a throughput equal to twice the throughput of a drive, and capacity equal to 4 of the drives. Any 3 drives could fail (in some cases 5 could fail) and the data remains intact. See if you can figure that one out. ;-)