Idiot explanation (others will fill in the details):
Raid effectively makes multiple physical disks available to the OS as a single disk. There are different ways to do this, but only three which are commonly used.
Raid 0:
Striping. Imagine taking each disk and cutting them into bands, then layering the bands into one disk twice the size of the smallest disk. This solution allows for an increase in speed (you can write to both disks at once, ideally doubling write speed). What it does is decrease fault tolerance. Specifically, if either drive dies the data from the other is worthless.
So faster speed, but higher instances of failure.
Raid 1:
Mirroring. Imagine one disk as a mirror of the other. Each bit is written to both disks, which provides a complete image to recover should either of the HDDs die. It will be about as fast as a single disk, but you only get half of the space you paid for (less if one drive is larger than the other).
So high fault tolerance, but a large decrease in storage space.
Raid 5:
Parity. This requires at least 3 disks, and generates a parity string for the data stored on the other HDDs on the last disk. In effect, any one of the disks could fail, without any data loss. Visually:
______Bit 1_____Bit 2_____Bit 3____
Disk 1 |_1____|___0____|__Par___|
Disk 2 |_0____|___Par__|__0_____|
Disk 3 |_Par___|___1____|__1____|
This type of raid does not offer performance boosts, but it does offer high reliability with a minimum of lost space. If you were to create a raid 5 with 4 disks you would have 1 disk worth of lost space, so less lost space as disks increase. It compares with Raid 1 as follows:
Raid level Disks % Space loss
1________ 4_______ 50
5________ 4_______ 25
1________ 6_______ 50
5________ 6_______ 16.7
1________ 8_______ 50
5________ 8_______ 12.5
So you choose Raid 5 for larger storage arrays, that still need reliability.
There are also a few things you should know about any Raid setup.
Hardware level raid is supported by either motherboards (starting at the medium end, and generally all high end boards support it) or expansion cards. This requires the disks to be formatted, so your data will be lost unless you're starting from scratch.
Software Raid blows, there is no more concise way to put it. It is slower, and if anything gets changed in software your data is up in smoke.
Raid arrays can only build from the size of your smallest disk. So if you have a 320GB, 500GB, and 1TB drive in Raid 5 you'll only see 640GB of useful data (these numbers are based on 1000=GB, like advertised on HDDs). In Raid 0 you will only see 640GB if you use a 320GB and 500GB HDD (the rest of the data storage is inaccessible). If you use Raid 1 you'll only see 320GB if you install a 320GB and 500GB drive.
In short, you either need to save money and get a 320 GB HDD if you are going Raid, or not use Raid. Given your lack of experience, and contingent upon the fact that you only presumably have one drive, Raid is not a good solution for you right now. Just get the 500GB and use it as a second storage drive.