A Box Clasp is usually square or rectangular in shape (hence the name) and comprises two halves of metal, one clips inside the other and the clips are released by pressing down on a little piece of metal protruding from one half of the clasp. Box clasps come in different sizes so you can string one, two, or three strands from them. There is a more secure variation, often used by professional jewellers where one half of the clasp has a hook that will catch onto a bridge of metal in the other half and then push inside that half, so this is doubly secure as even if the clip comes undone, the hook should still hold the jewellery.
Pros: Box clasps and slide clasps are an ideal option for multi-strand jewellery. They fasten securely and are available in a range of styles so can be incorporated into different designs. They are both reasonably easy to fasten and unfasten with one hand, so I find they are a good option for bracelet designs.
Cons: I have found that the fastening on a box clasp can become a little loose over time, so this may be something to bear in mind. The same problem can occur to a lesser degree with slide clasps as well. As with other types of clasp, this becomes less of a problem with a more expensive brand. If you are making jewellery for yourself then you may feel comfortable risking a cheaper brand of finding, but if you are making for customers, then I would advise buying top quality. You should be able to pass on the cost in the price you charge and it is more than worthwhile when it comes to creating good customer satisfaction results, which are so important for your reputation.
Claspgarten have a lovely range of designer box clasps that are decorated with pearls and crystals or can even be personalised. You can find some samples here.