There are a few reasons why domestic cats have better balance than people although there is an overlap in the anatomy of cats and people with respect to balance.
Both humans and cats have a vestibular apparatus. It is in the inner ear. It is made up of three fluid-filled semicircular canals. They are lined with fine hairs called cilia. The canals are positioned approximately at right angles to each other. When the cat moves, changes direction and accelerates the tiny cilia are moved by the fluid inside the semicircular canals. This sends sensory information to the brain which allows the cat to orientate themselves. In addition, there are two other chambers in the vestibular organ – the utricular and saccular otolith chambers – which function to provide information to the brain about gravity and linear motion.
Apparently, a cat’s balance is enhanced by the alignment between one of the semicircular canals and the position of the cat’s head.
Another aspect of the domestic cat’s anatomy and that of the wild cat species is that they are incredibly flexible. Flexibility combined with an abundance of fast twitch muscles allows them to make adjustments almost instantly which aids balance.
You’ve probably noticed that the wild cat species which live in trees or in high places on rocky surfaces have the longest tails in proportion to the rest of their body. I’m thinking of, for example, the snow leopard hunting on 40° rocky slopes in the Himalayas. I’m also thinking of the wild cat species who tend to live in trees i.e. are arboreal, such as the margay and the clouded leopard. Both these elegant wild cat species have long tails because they use them to balance. When a human needs to balance themselves they use their arms and perhaps legs to get back into balance because they can adjust the position of their weight. A cat’s tail achieves the same goal. You will also see the cheetah using its tail to balance themselves as they zigzag behind an antelope that they are chasing.
The domestic cat is famous for its ability to self-right when falling. This is not strictly a part of the cat’s ability to balance well but it does serve as a protection when a cat’s balance fails them. When domestic cat’s fall a sufficient distance they are able, within that timeframe, to ensure that their bodies are in a position to land on all four legs. This protects the cat. The physics of falling from a height are quite complicated. You will find that at a certain distance a cat is more likely to survive without significant harm because there is a terminal velocity and the cat is able to be in a position to land relatively safely.