The reason for the "tumble" is essentially what S_Baker stated.
The 5.56mm NATO ball (FMJ) is, depending on your views, either horribly designed, oversped and underpowered, or it‘s a fantastic, accurate and appropriate battlefield projectile.
The bullet itself is very small and light (being only .223 calibre, it is almost the same diameter as a .22 long rifle), and pushed through the barrel far too fast for its size. But probably the main problem, and the cause of the "tumble" is the shape of the bullet. In most cases, the tumble doesn‘t happen until after the bullet strikes something solid (ballistic gel, a human, etc). NATO, apparently, approves of this concept because the bullet is more likely to stay intact inside the target, yet cause a devastating and disabling wound as it tumbles through the target, leaving a wide permanent cavity within. Because of the small size and weight, the bullet is more likely to stay in the target, instead of pass through. The logic behind simply wounding the soldier is that it takes two to evacuate one, thereby removing three people from the battlefield.
I personally think this is flawed thinking, but then again, I am not a defence scientist.
The comparison is usually against the heavier and slower 7.62mm NATO bullet. This is the bullet used in Brit army FN‘s at the infamous "Bloody Sunday" incident in Northern Ireland, and one reason for the swtich to the 5.56mm standard. The 7.62 was found to be overpowered, and could often overpenetrate the target, striking other unintended targets behind the first one. The 7.62mm doesn‘t tend to "tumble" as much, and because it is larger in diameter, it leaves a larger wound cavity and is thought to be more lethal.
Of course, it is preposterous to grade bullets as "more" lethal, because it implies that some bullets can be "less" lethal. As we all know, you don‘t shoot anything unless you intend to completely destroy it.
For some interesting information about how bullets fly, check out this informative website:
http://www.nennstiel-ruprecht.de/bullfly/index.htm#Top_of_page
I must add my experience in this area is limited. I‘ve never personally studied the 5.56mm or the 7.62mm, although I have fired both as a recreational and military shooter. Most of my data is anecdotal, or from third-party sources who claim to be very well informed on the subject of military small arms. They have all said similar and consistent things, however, and so I have no reason to discount their ideas outright.
In short, the 5.56mm is small and intrinsically unstable. This has certain military applications, but may or may not be better than other small arms ammunition on the market, depending on your views.
