Let's consider two possibilities.
I know it seems unlikely that there is just one definitive characteristic which distinguishes us, so let's entertain two possibilities: one general possibility and another pretty specific one.
First, we'll say that what separates us from animals is our ability to manipulate the world around us. Second, we'll say that what separates us from animals is our unfortunate ability to ... well, we'll get there in a minute.
When you're a nonhuman ...
Imagine that you're an animal living in the wild. You eat what you can find. You sleep outdoors, of course. Perhaps you frolic in a meadow or swing from vine to vine in a jungle. And, oh yeah, you are naked.
However, you do notice that your food supply is becoming more scarce each year. The animals or plants you eat no longer thrive where they have for generations. Perhaps you and your herd migrate to wherever you can find food and shelter.
Searching for basic survival, you're in unfamiliar territory. Your herd is dying off, and you haven't seen another animal like yourself for as long as you can remember. You may not have the cognitive processing of a human, but you still somehow know: you must be the last of your kind.