Not surprisingly, in the sport of Boxing a body blow is any legal punch that lands above the belt and below the head. This includes the abdomen, chest and sides. Hitting in the back is illegal, and the arms are, of course, considered a blocked punch.
Boxing trainers seem to constantly train and then yell at their fighter during a fight to use body blows. If you are faced with a very quick fighter you can "take away his legs" with consistent blows to the body. If your opponent is good at moving his head and avoiding punches using body blows to "mix it up" can make him lower his defenses. Body blows can be thought of as "putting money in the bank" in a long fight. Over time they have a cumulative effect of weakening the opponent and setting them up for a KO. A fighter who goes through the early rounds head-hunting can find themselves at a disadvantage in the later rounds against an opponent who threw effective body blows. Body blows actually hurt more too. Supposedly, after taking the first few punches to the face it will get numb and not hurt so badly. A good body blow can cause some real pain each time it lands though.
On the other hand, very few boxers effectively use the body blow for various reasons. For one, it's not seen as a good way to KO and opponent. Very few fighters can actually stop a fight with a body blow. Also, some judges will ignore body blows. Many boxers don't want to possibly lose early rounds to increase the chances of winning later. Body blows are more difficult to land. This is increased by the fact that you have to be careful to not land a low blow. Many boxers who use lots of body blows get into trouble when a few go astray. The fans usually do not react to body blows. Since the fighter's head doesn't snap back or anything there's usually no major reaction to a good body blow. For all these reasons, until they really need to, many boxers will not develop their body attack.
Most info based on watching ESPN2's Friday Night Fights. Many of the phrases quoted are from Teddy Atlas, one of FNF's commentators and boxing trainer.