My statistics textbook at home covers this in pretty clear detail. I bought mine from abebooks for like 10 bucks, seems money well spent. Stats Wikipedia is written by and for stats PhDs. My recollection on standard deviation:
1. It's a descriptive statistic; we want to summarize how closely data clusters around its central ("mean") value.
2. We could just calculate the average distance, but we kind of want to penalize large outliers. We want the sequence [50,50,50,50,47,53] to have a higher deviation than [51,49,51,49,51,49], even though they both have a total distance from 50 of 6.
3. To achieve this, we use "root mean squared" -- square each sample's distance from average, then average those values, and finally take the square root of that average. In this manner, samples with large distances have a greater effect on the outcome.