We were intrigued. Apparently it's a practice that began in England in 1854 when a national park guide left his calling card in a bottle and invited those who found it to leave theirs as well. It's fairly new to North America, but could be a memorable and fun scavenger hunt with the kids...
It's kind of like a treasure hunt and the clues seem to be mostly on the website, Letterboxing North America. You can also find out more there about how to join in and what to expect.
Once you find a box, it will contain a hand-carved stamp, a log book, and possibly an ink pad. The finder stamps their personal logbook with the stamp they find, and leaves their own stamp in the logbook of the letterbox.
If you're kind of confused like we were, but want to learn more...check out Letterboxing North America, and a post about a first-hand experience from blogger Baroque Babies.