Remember when I said that links have value to search engine optimization? Like many things with value, it's not hard to picture an economy where links can be abused, sold, or traded.
One trick that the “bad guys” employ is to use automated software, similar to spiders to search out websites with comments sections. From there, it's a straightforward process to post comments with links back to their own site. Sprinkling in a bit of quasi-English yet nonsensical text, and it can even make it past many spam filters. Bam — lots of links, very quickly.
To combat this and other forms of link abuse, the nofollow tag was created in 2005. Basically, it gives website owners a way to tell Google and other search engines to not pass any value from that particular link. The theory was that if blogs were to employ it, spammers wouldn't waste their resources trying to spam sites, and their ill-gotten gains would evaporate.
Today, in 2012, link spam is still a problem, despite widespread use of nofollows, though it has subsided and it's effectiveness is greatly reduced.
Nofollow links can also be used to strategically manipulate link juice passed from links, a technique called "PageRank sculpting", although there are alternative ways to accomplish this goal as well.