I'm genuinely curious. I haven't yet figured out how being on Facebook could be a productive use of my free time, which is unfortunately very limited.

The basic functionality is simply to keep track of the list of interesting people, ideally with contact info automagically updating. Following the status updates is an extra that supports the sense of being in touch without explicit effort on your part, which can be made efficient if you block enough of the more prolific/uninteresting updates, and/or restrict the connections to people you know reasonably well.