Answer:

Two different kids, two different ages, same problem: head banging during a temper tantrum. It's very distressing to watch.

First, some reassurance. I have never seen (nor has anyone else I know, nor has anyone written about it) a child do serious damage to their head by banging it by themselves. They appear to be sensible enough to know how hard is too hard and to stop short of really hurting themselves. So that's good news.

But why do they do it anyway? That's a hard question to answer because by the time they have the ability to explain it to us, they don't do it any more. Therein lies a clue: Children who are too young to express themselves -- that is, to explain their frustrations and to verbally negotiate their demands -- become easily frustrated and fall out. That's one reason why temper tantrums are a developmental inevitability in toddlers.

There are other reasons that tantrums are so common. Toddlers have little ability to delay gratification. When they want something, they want it now! They are also egocentric and simply can't think of a good reason why they shouldn't be allowed to have or do everything they want to. 

Additionally, they have little ability to inhibit or dampen their strong feelings that come pouring out the floodgates without any ability to control them. Temperament also plays a role. Children with intense temperaments, for example, have especially dramatic tantrums. Children who don't like things to change have more frequent tantrums.

In time, almost all children slowly learn to deal with frustration in a more controlled, developmentally appropriate way. That's why I recommend simply making sure the child is safe (more about that in a second) and generally ignoring them during a tantrum. What you don't want to happen is for the child to learn that she will get a lot of attention for the tantrum. In that case she may continue to have them just to gain your attention. 

Avoid frustrating experiences when possible (lots of luck with that!), but when the tantrum comes -- as it surely will -- let it pass, like a summer squall. Don't carry a grudge, just move on when it's over.

Most of you will have noticed by now that I still haven't answered the question of why children bang their heads. That's because I don't really know. I'm guessing that there's something about the feeling that the child enjoys. It certainly gives you a new perspective on things and it certainly serves to shut out the rest of the world! (There are some normal toddlers who bang their heads on the mattress every night to get themselves to sleep.)

I would advise that, whenever possible, you make sure the head banging occurs on a carpeted area to avoid any bruises. Then just ignore it as you would any tantrum. I don't know of any way to convince them it's not in their best interest to bang their heads. And, remember: if you pay too much attention to the head banging, you just might prolong this troublesome behavior.