First of all RAID is not a substitute for a good backup strategy.

There are basically two concepts one uses distributed copies (RIAD 1 - also called mirroring, data is organized in blocks and every drive contains the same blocks) and another striping (RAID 0 - mostly done at block level with block level striping).

One advantage of mirroring mode (two or more drives holding the same data) would be, that you can easily get snapshots and backups from the system by just removing the drive from the system and archiving that drive. This seems like a poor mans backup and snapshot strategy since there are more sophisticated mechanisms available nowadays but that's still a nice example for using redundancy.

Another benefit of mirroring is that you can execute as many read operations as you have drives in the array at the same time. Linux software RAID has that capability, but for writing every drive has to write the same data.

With striping data is organized in stripes that cover two or more drives, so that workload can be distributed across multiple drives. The array is faster but offers no redundancy.

To have the benefit of both modes one can use combined modes such as RAID 10, which uses distributed copies of striped blocks. But this comes at the expense of using even more drives to store the same amount of data.

RAID 5 uses only striping but manages to keep redundancy by calculating parity data. It has different characteristics than RAID 10 and it's not always clear which mode serves a task better, sometimes it's RAID 5 and sometimes it's RAID 10.

Though on personal experience we had a failed RAID 5 array at work in a customers machine because somehow errors got into the parity data and the only way out was to set up a new array. Of course the colleagues ignored the advice from the qualifier at that time and just replaced one drive, but a month later the array was dead and lost.

Apart from Wikipedia I would recommend reading the Linux RAID Wiki as well as the manpages of mdadm and md.