There's no one answer, so...
Since this is the Philosophy forum and bending the rules is one of the rules, I'm going to give three answers. But there's continuity here, so humor me. You'll love the ending.
First, starting 60 million years ago.
A whole new class of plants sprang up. I think they're called angiosperms, but I'll let the biologists verify that. What they were was the first trees with fruit on them. The birds and the flying insects got an instant banquet. But there were no mammals that could climb a tree.
(Maybe there were predators with claws like the modern felines who could do it, but:
1. I doubt it. The sloths that are about to debut and play a key role in this story were small and slow. They'd have all been eaten.
2. Their digestion was too specialized for eating meat. They probably couldn't eat fruit anyway.)
Some of the mammals looked longingly up at that bounty and tried to learn to climb trees. Eventually the sloths evolved. Small, slow, weak mammals (fruit isn't exactly laden with protein), but they could climb trees, making them safe from predation, and they had all that fruit to eat. The primates are descended from the sloths.
So all of you Atkins dieters who are trying to delete fruit from your diet? You're fighting sixty million years of history.
The first thing that makes us human is our love of fruit.
Fast forward about 54 million years.
For whatever reason, and you can find a dozen threads on SciForums with suggested reasons, some of the chimpanzee-like apes decided to come down out of the trees and live on the savannah. Life was tough there for herbivores, because there were already elephants and giraffes and rhinos and buffalo. Lots of big, strong, fast mammals that already laid claim to the plants of the savannah. The apes would probably have had to go back up into the trees until one of them got a brilliant idea: Hey let's just eat the herbivores! They're everywhere! Why try to survive by eating grass when meat is so much more nutritious?
I've seen baboons on nature shows watch hyenas run into the water and catch flamingoes and then learn to do it themselves. I'm sure our ancestors did the same thing. Eventually they invented spears and learned to drive their prey into cul-de-sacs, and finally (hooray) how to cook the damn stuff. With a steady supply of meat, they were able to stay on the ground, learn to farm, build houses, and eventually computers.
So all of you PETA types that think we shouldn't eat meat? You are fighting about six million years of history.
The second thing that makes us human is our love of meat.
Now fast forward about 5,988,000 years.
Humans have spread all over the globe. There were human hunting parties everywhere. The wolves, successful pack-hunters who were also everywhere, couldn't help but notice that the humans were really good at it. They could formulate and communicate extremely complicated plans, and they could bring down unbelievably enormous prey like mastodons that wolves could only dream of. But they were extremely wasteful, inexplicably leaving pieces of perfectly good food lying all over their campgrounds. And possibly most wonderful of all, those same campgrounds also had nice warm fires.
The humans in turn couldn't help but notice that the wolves could smell prey that was much further away than they could see. With their sharp teeth and claws they could just about bother an animal to death once they got it surrounded. They were absolutely fearless protectors and would risk their lives to run off lions and bears from their own camps. And by golly, they just loved to eat garbage, which really cut down on the bug problem.
A marriage made in heaven. No one domesticated dogs, they just started hanging around and the humans let them, as long as they learned not to eat the baby humans when nobody was looking. The dogs were cool with that, considering all the free garbage to eat, and in fact they were happy to protect the baby humans and their mothers from bears and lions while the male humans and the rest of the dog pack were out hunting gigantic tasty animals together.
(I'm calling them dogs at this point instead of wolves. They are actually not two distinct species. The only real difference is that wolves are still wild. Oh yeah, and dogs have evolved slightly smaller brains so they can thrive on the lower protein diet of a scavenger. Their DNA differs less than an Irishman differs from a Maori. Wolves are really just one breed of dog: the oldest.)
Two species of animals that ran in packs, had a social hierarchy, had complementary hunting skills, and between them did a great job of running a safe, warm, clean campground. It wasn't long before they regarded each other as companions. Everybody loved puppies, and young humans would curl up with the dogs at night to keep warm. The rest is history.
And that, my esteemed fundamentalist Muslim friends, is the particular twelve thousand years of history that you guys are attempting to turn your back on, with your absolutely ridiculous ideas about dogs having no place in a human home. Our relationship with dogs goes back ten thousand years before Mohammed was a gleam in his father's eye. And it has never caused a war! In fact, the medical community continues to discover new situations in which dogs relieve stress and make us more peaceful. If you want to create a religion, it's dogs we should be worshiping.
Dogs and humans were the first multi-species community ever to occupy this planet. (I'm not counting biological relationships like parasitism -- fleas and ticks -- and symbiosis -- those birds that keep the hippos' teeth clean.) Humans learned to live with, respect, care about, and eventually love, "people" who belong to a totally different species. That was a powerful lesson to have behind us when we finally got to the point where we outgrew our tribal villages where everybody knew each other, were related, and shared the same beliefs. Could we have built cities where we had to get along with people who were different from us? Could we ever have built nations including people who are so different that they don't even speak the same language or believe in the same prophet? Could we have done any of that without the experience of learning to live with companions of a different species? Considering what a rotten job we're doing of it as things are, practically blowing ourselves off the planet every couple hundred years, I really doubt it. We have dogs to thank for the fact that civilization exists at all.
The third thing that makes us human is the multi-species community we built with our dogs.
What makes us human?
1. We love fruit.
2. We love meat.
3. We love dogs.