GPS thingy is like a car sat-nav but you carry it around with you on walks and stuff, for navigation, plus it keeps a memory of your route which you can download onto a map (or somesuch, I'm not very savvy about it). It basically gives you GPS coordinates (you can use it in the car too).
Geo-caching is an odd activity that I came across via mumsnet. People go out and 'hide' a sealed container full of bits and bobs. They then post the coordinates on a website and other people go out with their GPS units and try and find them. They open the pots and exchange some bits for some more bobs. Then they go online and post that they visited it. I hear that it is fun if you plan a walk to look up what caches there are and visit them. Good for kids as they love the bits-and-bobs stuff. Some of the stuff likes to tavel, so you tke it out of one cache and put it in another (preferably far away) and then say so online. Some of the stuff travels round the world.
My DP will love that kind of stuff.