It's all right here really. But here's my take on Letterboxing.
A letterbox is generally a smallish tupperware type container hidden in an inconspicuos space at in interesting location. Most are in wonderful natural settings -- parks, hikes, scenic overlooks, etc. But some are in urban settings. In the letterbox is a stamp (sometimes hand carved) and a small journal. Sometimes there is also a stamp pad and pen or pencil. All letterboxers have their own personal journal and stamp.
So, when we find a letterbox, we pull out our personal journal and stamp the stamp from the letterbox in our journal. I make a note of the date and location. It's a bit like a passport. Then we stamp our personal stamps in the journal that was in the box so when others find it, they can see that we've been there. Sometimes we write a comment about the day or the location or the stamp or whatever. We also puts our names, where we are from and the date.
Most letterboxes and the clues to find them are listed on the main letterboxing site. Some clues are easy and obvious, some are complicated and obscure. There are more than 15,000 boxes listed on that site.
I don't know why exactly it's called "letterboxing," since there isn't really a "letter" involved. At least not specifically. One time I was listening in to Claire telling one of her friends about letterboxing. She said, "Do you know what a letterbox is?" The friend replied, "Sure, we have one for our cat."
The thing I love most about letterboxing is that it gets us out to places we might not have discovered without the "mission" of boxing. Go out and box!