Raid 0 increases performance by writing consecutively to both drives. For instance, lets say the data is the alphabet and you have two drives. The data would be then written as follows; Disk1>A, Disk2>B, Disk1>C, Disk2>D, and so on and so forth. Now, while this does create a faster read and write it also means that you have an inherently unsafe setup. If one disk fails on the stripe, the stripe is then broken and your data is corrupt.
Raid 0 also allows you to combine the storage space of 2 drives into one logical drive. So if you have 2 300gb drives in a raid 0, you will see only one 600gb disk.
Raid 1 is primarily used for redundancy. Where in raid 0 you write one bit to each drive consecutively, in Raid 1 the disk writes to the first drive and copies the data to a second redundant drive. If one of the drives fails at any point in time you have a backup copy of all your data on a second drive, which usually will take over the instant the first one fails. One drawback of this is the size of hdd to cost ratio. If you have 2 300gb drives your system will only see 1 300gb drive. However, if your data is that important to you it's sometimes worth a little extra money for data safety.
If you want to learn more about raid and its different benefits/cons and configurations visit http://www.acnc.com/04_00.html.