Koalas have tough granular skin on the palms and soles of their hands and feet that gives them very good grip.
Their hands and feet are very muscular and strong. Their digits are quite long, with large rounded pads at the tip of each finger/toe. They have two opposable thumbs on each hand, which gives them a more powerful hold around a branch.
Like us, koalas are large mammals that spend a lot of their time upright. They live primarily in trees (as we once did, and most of our primate relatives still do) , but unlike monkeys and possums, they lack a tail and are relatively heavy and solid in their body shape. So their means of getting around in a tree is very like a primate’s – they climb using power and intelligence, rather than lightness and agility, to get to where they need to be. Their hands and feet, like ours, have developed due to their lifestyle.
It is interesting to watch a koala handling a branch full of leaves. They grab in exactly the way we do. Having dextrous hands gives them a very human aspect (which might explain why we find them so appealing!)
Interesting, too – koalas have individual fingerprints. Once thought to be a primate attribute, this is another thing that koalas share with us!