A goatee is a narrow beard. If your uncle shaves his cheeks and the sides of his chin, leaving just a strip of hair under his mouth, you can compliment him on his goatee.
Some facial hair purists say that it's only a goatee if there's no mustache involved — the combination of a narrow beard and mustache can also be called a "Van Dyke." Others are fine with describing any beard that doesn't extend fully across the face from ear to ear as a goatee. This term comes from the tufted beards that many goats have, and it was originally known as a goaty.