To nuzzle is to affectionately rub your nose and face against someone (or something). It's hard to get out of bed in the morning when your cat lies down on your chest and nuzzles you.
A mother might nuzzle her new baby's head, and a horse will nuzzle a person's hand — hoping for an apple or sugar cube. In the fifteenth century, this word instead meant "to bring the nose to the ground," from the verb nose, "pry or smell with the nose." The current meaning was influenced by words like nestle and the now-obsolete "nursle," meaning "to nurse."