Speed gains in a RAID configuration depend on the RAID level. Most common are RAID0, RAID1 and RAID5, which are the archetypes for any variations in RAID levels.
The idea behind RAID0, or "a striped array", is that files are split up 50:50 (in case of 2 drives, 25:25:25:25 in case of four drives) and can be synchronously written and read in approximately double (or quadruple) the speed of a single harddisk. The biggest caveat for RAID0 systems is that when one disk fails, you cannot recover the missing 50 or 25% of the original file, so you practically lose data on both disks.
The idea behind RAID1 (mirrored array) is redundancy: Every file is stored twice on 2 drives or four times on four, etc. This doesn't give you a backup of your data (since you can "destroy" data by accidentally deleting it), but it gives you redundancy in terms of the disks: If one fails, you still have the exact same data on the other disk.
RAID5 combines both concepts, in the sense that data is distributed among at least 3 disks. Data and parity information is distributed among those disks so that in the event of a drive failure everything can be restored, no matter which disk fails. This redundancy limits the available space for data on the disks, if you use 4 disks with 500GB each you get 1500GB usable space in comparison to 2TB if you didn't use RAID5. RAID5 is typically handled by expansion cards, since the concurrent mirroring and striping activity is somewhat computationally expensive (meaning that a dedicated chip delivers better performance). Newer logic board chipsets can handle the extra load, but in general it's recommended to use an extra SATA/SAS card (mostly out of compatibility and recoverability concerns).