Purchasing Keywords?

I'm not sure I understand the activity of "purchasing" keywords for advertising in Adwords. In the past when class members have managed Adwords accounts for non-profits, we simply entered relevant keywords and keyword phrases that we thought users would search for. It appeared more like the keywords were what drove traffic to the text ad that was created. Only when users click on the ad was the account for the non-profit charged for the click. Is purchasing a keyword something different all together or are Adwords users in effect paying for the keyword as well when the ad is clicked on? It seems like it would not make much sense to pay for a keyword when it could be used in Adwords to drive traffic to your site.