Hairy things are furry or fuzzy — covered with hair. If your hairy dog lies on your bed, your bed may end up hairy as well.
If your dad has a bushy beard, he has a hairy face, and while some kinds of caterpillars are sleek and smooth, others are hairy. Informally, you can also use hairy to mean "scary." The biggest roller coaster at an amusement park will probably have a few hairy loops and turns. This slang meaning has evolved from its original use as "difficult," dating back to the 1840s.