Anatomists examining koala forepaws in the 1990s found dermatoglyphs, the raised skin ridges that make fingerprints, arranged in loops and whorls closely comparable to those of humans and other primates. Koalas and primates last shared an ancestor well over a hundred million years ago, and no intervening marsupial lineage shows the same detailed pattern, so the resemblance is convergent rather than inherited.
The likely function is grip and touch. A koala selects individual eucalyptus leaves with its hands, using two opposable digits on each forepaw that work against the other three, and ridged skin improves both friction and the resolution of fine tactile information.
The frequently repeated version of this fact, that koala prints have been mistaken for human prints at a crime scene, has no documented case behind it. The published claim is only that the two are hard to distinguish under casual microscopic comparison, which is a statement about anatomy and not about forensic practice.