Humans have several unique qualities (and many more not-so-unique), but one that may not come readily to mind is that we throw things, and we throw them very well. No other animal we know of could come remotely close to doing this, or this, or this. Even an average human's throwing abilities are far beyond anything else in the natural world. If I said that I'd seen someone throw a ball 50 meters, no one would think twice. If I said that I'd seen a horse throw a ball 50 meters, the most likely response would probably be "No, you didn't", maybe followed by "How??"
If you think about it, it's actually somewhat surprising that humans would be unique when it comes to throwing things. It's a very useful skill. If you can bring down a small mammal with a well-aimed rock, you'll eat much better than if you have to run it down. Even if you're a very good runner-downer, it still takes way less energy to throw a rock. Throwing a rock can also get a high-hanging fruit out of a tree (though not easily). Throwing is a good way to get something you're carrying up onto a high ledge that you can then get to with all your limbs free, and so forth. You'd think something would have stumbled on it before our ancestors did.
On the other hand, a lot of body plans just aren't that well suited to throwing. Birds have one set of limbs serving as landing gear and for locomotion when not airborne, and the other given over to wings. That leaves the head and beak as all-purpose picker-uppers, severely limiting throwing potential. Birds can throw things by picking them up and then heaving the head and letting go, but not very far or forcefully.
Fish and other sea creatures live in a viscous medium where throwing is not particularly useful. Most mammals have all four limbs specialized for walking, running, jumping and so forth, leaving them in much the same spot as birds. Lizards are also pretty well tied to the ground or other surface they're traveling on -- particularly the limbless ones, to say nothing of actual snakes (snakes are closely related to lizards, but there are also some proper lizards that lack limbs).
There's an obvious common thread here: To throw effectively you need a free limb, one not specialized to supporting your weight. You need hands, as opposed to front feet. You don't need to be fully bipedal, though that clearly ought to help, but you do need to be able to grab something, stand up on your hind limbs and let fly.
There aren't many animals in that category, but several primates are, by virtue of having hands (and feet, and tails) adapted to grabbing and swinging from tree branches instead of always walking on all fours. Putting all this together, perhaps it's not so surprising that throwing would have only evolved recently, in a branch of the primate family tree, itself relatively recent.
It is a principle of evolution that behavior tends to change first, and then anatomy follows. First certain fish started coming up out of the water, whether to escape from other fish who couldn't or to move from a shallow, drying-up pond to a deeper one, or for whatever reason. Later came Tiktaalik and its kin with pectoral fin bones (and other features) better adapted to life out of water.
Once the new niche was established on land, there was plenty of selection pressure to reshape the body for living on land, and eventually lose the older adaptations for water living entirely. More strictly speaking, the new behavior of coming up on land meant that fish with more land-adapted bodies could have better survival chances.
In the case of primates throwing, it's not that other primates don't throw. Some species of monkeys are well-known to throw excrement at others of their species, and chimps will throw things as a threat. It doesn't seem to matter much to them what they throw, but it will generally be branches and occasionally rocks. Chimps don't show signs of throwing with the same purposes we do, but it's significant that some sort of throwing behavior is established in our near relatives. It's therefore plausible, though not certain, that it was also established in our common ancestors.
While chimps are known to hunt, and are known to throw things, and are known to be reasonably intelligent, they are not known to throw for purposes of hunting. This is not completely shocking, as they tend to hunt small monkeys in trees when they hunt. The strategy is to go in as a group, block off escape routes and send one member of the hunting party in for the kill. Rock throwing would probably not help much in such a situation. You'd have to encumber a hand carrying a rock up into the trees, and then you'd only have one rock, a bunch of branches in the way, and a monkey that would not be well-inclined to staying still in the path of a hurtling rock.
But imagine a tribe of ancestral chimps a couple of million years ago venturing out of the forest. These wouldn't be exactly like today's chimps, of course, but today's chimps appear to resemble these ancestors much more closely than we do, so we can consider them ancestral chimps here. In 1993, William Calvin laid out a hypothesis that a good way for such creatures to get food would be to stake out a water hole and go after the herds that gathered there to drink -- as several other predators do.
Naturally, herds of gazelles and such are adapted to dealing with predators around water holes. The main strategy is to stampede away, which works well, except that any animal that trips or falls is likely to be trampled by the herd and left behind as an easy meal. This actually works reasonably well for the herd as a whole (from an individual's view, if you have this behavior you're more likely to be one of the survivors than if you don't), and it works for the hunters as well. It just doesn't work particularly well for the particular animal left behind.
Now suppose you hit upon a way to make a herd stampede, and at the same time make one of its members stumble and likely be trampled. That would work even better for you, though again not so well for the unlucky victim. Calvin's idea is that there's an easy way to do this, that those ancestral chimps could have done with the mental and physical abilities they had: Throw a reasonably-sized rock into the herd. If it hits one member, that member will stumble, the herd will startle and, with a bit of luck, trample the stumbler. This doesn't have to happen every time, just enough to make it noticeably easier to get food from the herds gathered at the water hole.
At that point, we're off to the races. Any change, whether in behavior or anatomy, that improves throwing force or accuracy, will make for better hunting and better-fed primates. Richard Young cites paleontological evidence to support a claim that exactly this happened during the past couple million years -- the body, and the hand in particular, became better and better suited to throwing (and to clubbing, another area where we excel). Doing these well requires a number of changes from the long-fingered, short-thumbed tree-branch-hooking hands of the rest of the chimp family.
Calvin, for his part, speculates that the famous Archeulean hand axe was actually an improved weapon to throw into a herd, as it would be more likely to cut into the prey's hide and cause it to instinctively collapse, making it more likely to be trampled. As always, this doesn't imply that the hunters were thinking it through in that much detail. It's enough that throwing a sharp rock works better than throwing one that isn't, and that some in the population had an innate proclivity for chipping away at rocks and so making them sharper.
It's been argued repeatedly that, if we weren't the ones doing the classifying, or weren't so subject to a certain prideful feeling of distinctness from the rest of nature, we would be classified in the same genus as chimps and bonobos. Either they would be Homo troglodytes and Homo paniscus, or we would be Pan sapiens. Under the latter scheme, those savanna-dwelling rock throwers might best be called Pan proiiciens -- throwing Pan, the name Pan being taken from the Greek god of the forest, used to designate the forest-dwelling chimps and bonobos. Except these particular Pan would be leaving the forest.
Behavior drives anatomical change, but anatomy limits behavior. Just as only some fish had the right anatomy to even try moving on land, only some animals had the right kind of body to try throwing things. Primates happened to be close enough, again likely because their hands had already adapted for something else besides walking, something that allowed for grabbing and flinging. This is a common pattern in evolution. It used to be called pre-adaptation, but that gives the impression that, for example, primate hands evolved for grabbing tree branches so that they could later evolve for throwing and clubbing. That's not how it works, so the ungainly but unbiased term exaptation is preferred.
There is another interesting point that Calvin makes. It's not enough to have the anatomy. You need to be able to control it. It takes around a tenth of a second for our bodies to carry out a conscious command. To throw a projectile accurately [as we do now, as opposed to lobbing rocks into a herd -- D.H. Sep 2015], you need to time your movements within about a hundredth of a second. Once you've decided to throw something, it's far, far too late to make adjustments as you go along. You have to have the whole program ready to go ahead of time, adjusted for where your target is -- or will be when the projectile reaches it. Calvin speculates that this sort of plan-ahead was re-purposed into our control structures for things like language.
I'm not sure I quite buy this. I doubt that throwing is the only thing in evolutionary history that requires this sort of plan-ahead. Surely when a hawk dives for a mouse or a cheetah jumps for a gazelle it is doing the same sort of thing under similar constraints. Nonetheless, it's an interesting idea, and plausible in a general sense, that the original behavior change of throwing things would have brought on a host of other changes, in both behavior and anatomy, that led to wholly new behaviors like speech and large-scale planning (for lack of a better term for the type of planning that we do and other animals don't).