Most animals look almost identical to their peers. To distinguish lions we record the spots on their face; with whales we look at the blemishes on their tail or flukes. In other words, we have to try hard to distinguish one lion from another.
In the case of dogs, we have created many different looking breeds - but within each breed they look the same: one poodle looks very much like the next one.
On the other hand, with humans we have not only the different races (cf. dog breeds), but even within one race no two people are alike. And, not only are the faces different, the body shapes vary equally much. We use face and body shape (and voice) to recognise each other. Most other animals use smell or sound.
I thought the reason for our uniqueness might be that, with civilisation, we are not constrained us to look the same. However, even in hunter-gatherer tribes each person looks different from every other one.
So what is it in human evolution that made us unique in this regard? And, are we unique? I cannot think of any other species with as much variation as ours, but are there others?