Spining the arrow is essential to good arrow flight. You can't see it very easily with the naked eye but the arrow flexes wildly when it is loosed. Take a look at this slow motion video and you'll see it:
http://www.youtube.com/watch?v=96KGWC0PB6s&list=TLZUlDXn_25A8
The arrow's spine measurement is basically a measurement of its flexibility. As Pat said, that flexibility needs to be matched to the bow's power and a number of other factors. If you don't use a properly spined arrow you will likely be doomed to poor arrow flight and quickly frustrated in your archery goals.
Guy