According to popular legend, the name of the boxer breed came from the fact that the dogs tended to begin fights by rearing up on their hind legs and striking at other dogs with their front paws. Very little support is given to this name origin, as many linguists have noted historical records which suggest that the name most likely comes from other sources such as nicknames of similar breeds or simply the names of some early well-known specimens of the breed. With the origin of the name and the accuracy of the legend in question, one must stop to ask, do boxers really box, or is that simply another legend that has arisen because of the breed's name being associated with the sport of boxing?
The answer to this question is a complex one; depending on how you look at the boxer's activities, you might consider it to be either yes or no. While some boxers do tend to play and assume a boxing pose, they are also generally gentle dogs and don't often begin fights in such a manner. If they do fight, some boxers may assume a boxing position but it is usually more an attempt to knock down or subdue the other dog than it is an actual boxing-type attack. These dogs are just as likely to make the same sort of biting or jumping attacks that you would expect other dogs to make.
One reason that boxers may have developed their renowned boxing stance during play is because of their lineage and original purpose. Boxers were originally bred as hunting dogs for use in bear and boar hunting, animals which are generally much larger than standard hunting dogs. Because of this, the boxer was bred to be a muscular and energetic dog that would have the power needed to be able to tackle a wild boar or to keep a bear off of its guard. It's likely that dogs which assumed the typical boxing stance while trying to take down larger animals were highly prized by bear and boar hunters, so those dogs were chosen for breeding purposes while the boxer breed was still being developed and refined. Much like dogs of pointer lineage will assume the iconic pointing stance even if they haven't been trained to do so, modern boxers may mimic their ancestors hunting techniques in their play.
Even though boxers don't actually box when fighting, the breed has a variety of other characteristics that endear them with owners around the world. Those boxer owners who wish for their dogs to learn to box for show or play purposes should have little difficulty in getting the dogs to do so, as they are quite intelligent and can learn a variety of tricks including boxing quite easily.