(noun) - Genre -- typically immediately followed by the word "painting" -- is most frequently used in art to mean "a scene of everyday life." A genre painting has a person (or people) in it doing something. Not a great big important something, either. Your basic genre painting subject is bound to be plucking a chicken, lighting a pipe, delousing a child's head or some other equally unglamorous activity.
In this context, genre was introduced and perfected by the Dutch Baroque painters of the 17th century. Think of anything Vermeer ever did.
In the mid-19th century, in the United States, "genre became its own separate entity (for a time), through the works of painters such as Winslow Homer, George Caleb Bingham and Eastman Johnson (to name a few).
Note: Just to throw a little chaos into the mix, "genre" also refers to a hierarchy of types of paintings instituted under the Academy system. And, yes, Genre Painting is one of the types. If you are thoroughly confused at this point, please see the "Hierarchy of Genres." The list there will explain everything.
We'll officially skip all of the non-visual art meanings of genre, which are legion. No need to further muddy the waters, is there?