Answer:
A koala is a marsupial. Marsupial young (called joeys) are born very undeveloped, completely blind, hairless and vulnerable. The joeys crawls by instinct to its mother's pouch, where it latches onto a teat which then swells in its mouth, securing it there. The joey completes its development in the pouch, emerging for short periods after a few months. This is the case with koalas, kangaroos, wombats, Tasmanian Devils and possums, to name just a few marsupials.
Koalas belong to a order of mammals called Marsupialia or marsupials. Marsupials brood their young in pouches. Bears belong to the order Carnivora (or carnivore) and then the family Ursidae. They are most commonly related in the fact that they are both mammals. Bears are placental mammals.
The bear in "koala bear" probably comes from the fact that it looks like a teddy bear -- but teddy bears really don't look like real bears. The concept of a teddy bear came from a cartoon of Theodore Roosevelt shooting a cartoon looking bear in a comic strip back in the early 1900s.