A genus-differentia definition is one in which a word or concept that indicates a species--a specific type of item, not necessarily a biological category--is described first by a broader category, the genus, then distinguished from other items in that category by differentia. The differentia of a species are the species' properties that other members of the genus do not have. In short, the genus is the broad category, the species is a type within that category, and the differentia are the distinguishing characteristics of the species.
Under the "genus" and "species" description, this sort of definition is used to categorize different plants, animals and other things into biological categories. See also genus and species and Linnaean taxonomy.
This can be clarified with a hackneyed example. Suppose we wanted to define the phrase "human being." Following the ancient Greeks (Socrates and his successors) and modern biologists, we say that human beings are members of a species. So we ask what the genus, or general category, of the species is; the Greeks (but not the biologists) would say that the genus is animal. The genus, then, is animal and the species is human being. What are the differentia of the species, that is, the distinguishing characteristics, that is, the properties that human beings have, that other animals do not have? The Greeks said it is rationality: the things that humans have that other animals do not is rationality. So rationality is the differentia of the human species, according to the ancient Greeks; thus Aristotle said, "Man is the rational animal." By this he meant to be giving a definition of "man," or of "human being."