I think i've narrowed down 3 qualities which make up the difference between animals and humans. Plenty of animals have these characteristics or abilities but not nearly to the degree humans have it.
They are Curiosity, Memory, and Pattern Recognition.
There are curious animals but humans curiosity seems to beat animals by several powers. While an animal might just check out something limited to their particular interests: possible predators and prey, and only check it out once or twice, humans curiosity seems to span to every topic, and can last a life time.
Animal memory is better than we give it credit for. They can learn plenty of things that last a life time, and what they remember can be disarmingly complex, but most of that is implicit memory. They know what they want, and their body remembers how to move to get it, but they couldn't call up that memory like we can(mostly a guess). An example of implicit memory is if someone suddenly chucks a ball at you and you lift your arms to catch it, and then they motion to throw the ball at you and you lift your arms premptively even if they don't actually throw it.
Humans have an abundance of explicit memory, that is memory of ideas and events that they can call up on demand. And I think this is a relatively new thing in evolution, because we have both explicit and implicit memory, and people we normally say have excellent memories have incredible explicit memory.
The last is pattern recognition. This applies both to recognizing patterns in our environment for the purposes of learning, and for the purposes of knowing how to react to those patterns. Animals have plenty of pattern recognition abilities; they have plenty of problem solving ability. It is often surprising how "smart" animals can be when it comes to problem solving. But due to humans curiosity, we are motivated to find patterns in everything.
Our learning ability could come from these 3 things. But what I think is really the key to get the engine started on what makes humanity go so far is curiosity. We are so curious we will make up problems for us to solve: games.
All the other qualities we have are pretty much common to all animals.
A couple of other things. I believe that schizophrenia comes from a screwed up or overpowered pattern recognition engine, among other things. The paranoia comes from a series of instincts that help the organism survive. When these two things come together, it helps delusions form.
And one more: I got the idea of curiosity being part of the key when watching of all things Terminator 2. I mean i have a dozen robot trying to be human movies, and it took a minor little touch in terminator 2 for me to start thinking it was really important. After the terminators switch gets reset, and he starts asking questions like, "Why do you cry?" It hit me. One quality of what we consider to be sentient beings is definitely curiosity, it is a quality that is abundant in children, it was even in one of my robot movies: Iron Giant, as a big major point of the plot. And it is a quality that seems to be totally missing from current AI programs. Chat AI's and other AI's all are reactionary, they wait for you to stimulate them and then they try to select an appropriate response. Humans on the other hand specifically seek out stimulation.