Often mistakenly referred to as Chinese puzzle boxes, puzzle boxes are actually a Japanese invention, dating back to around the 1830s.
A puzzle box is a wooden box, usually decorated with a inlaid pattern and finished with lacquer. They come in a variety of sizes and are traditionally measured in the Japanese units "suns". One sun is about 1.22 inches. Boxes range in size from 1 sun to 7 suns, with 5 being the standard.
The puzzle is - how do you open the box? The boxes usually have several sliding panels. In order to slide the lid off, the other panels must be slid in a certain way, in the correct order.
A simple measure of the difficulty of a puzzle box is the number of moves required to open it. I have an eight-move puzzle box, and that can take a puzzle-box virgin a good half-hour to figure out. Some people, of course, seem to have a talent for it and can open it in five minutes first time. (My Uncle demonstrated this ability, much to the chagrin of my Dad who'd got nowhere with it in the previous twenty minutes). I've seen boxes advertised with over fifty moves.
They aren't just puzzles, though, they're also works of art. You might easily find an expensive puzzle box which has only two or three moves but beautiful carving or lacquer.
Personally, I am more attracted to those with a really ingenious opening mechanism. I have two. The newer one has a lovely picture of a camel on the front, made out of different coloured volcanic sands. It's really only a one-move box; you just have to figure out where to apply pressure and the inner drawer slides right out. My other box has a simpler lacquer pattern but a complicated eight move series, cleverly designed to be completely non-intuitive, such that you sometimes seem to be going back on yourself and closing the box further in order to get it to eventually open. This is my favourite because it's so devious.
Puzzle boxes are not really practical for storing valuables, since a determined thief could easily destroy the wooden box. (I store sweets in mine so that any guests that pick them up and manage to get them open can have a reward). Their real charm is in the craftsmanship and ingenuity of the puzzle mechanism. Since they're hand-made, they tend to be expensive, which is a pity, since I have a strong urge to collect as many different ones as I can lay my hands on.