Since only half the data is written on each drive, there is less waiting for the cylinders to rotate and the read/write head finding sectors. While one hard drive is searching for bits it needs, the other hard drive can already be sending them. AFAIK, the HDD controller will reassemble them for use by the CPU/memory/whatever. There is really a lot less waiting - plus, both drives are able to stream data at the same time.
Assume this: one 20GB hard drive can put out, say, 20 MBps (an estimation). So if it wanted to read a 20MB file, it could take it a full second. If you're reading the same 20MB file off two separate disks, each containing half of the file, each drive will only have to read 10MB of data, roughly cutting the time in half (theoretically). Although real RAID isn't quite this efficient, some setups come pretty close.
What you were thinking about is what's called mirroring. This would read and write the same data to two separate drives, and this type of RAID array (RAID 1), all 20MB need to be taken off each drive in order to get the file, resulting in it taking the full second. This configuration is for redundancy, not performance. It takes no longer or shorter to write/read info in this configuration.