First serial rights for magazine publication used to be the only way to go in book publishing. Think Dickens, Trollope (a great writer currently undergoing a revival) et al. I'm using "magazine" a little loosely here, many of the serials that publish stories and book excerpts are really newspapers or newsletters. The attraction for the writer is making some money up front, often before a book is even finished, and lining up potential book customers if the excerpt is well received..
Last week, basically on a lark, I e-mailed an unsolicited proposal to the editor of a highly specialized computer magazine suggesting they might be interested in the first serial rights to some technical material I've been working up. My pitch to them, since it's reference material and could be spread out over a year's worth of issues, is that it would help retain subscribers and give the magazine a long shelf life, which should be attractive to their advertisers. On my side, I'd get paid some cash and get a free promotion for the book, assuming I published one.
One of the dumbest moves I ever made in publishing was giving a niche magazine the rights to publish an excerpt from a book without making any stipulations as to the timing. They used it in the first available slot, which means it went out to their 100,000 plus readers a full year before the book was available. That's about tweleve months too long for the purposes of book promotion.
Selling first serial rights to a print magazine, or even donating them under some circumstances, can be a great way to promote your book and to build your resume as a writer. The only thing I'd be cautious about is making sure that if the magazine has an online version, the article is either linked to your website or included in their robots exclusion file. Otherwise, it may appear to be duplicate content and compete with the version on your own website, hampering future book promotion efforts.