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."
However, the use of the genus-differentia definition is by no means restricted to science. Rather, it is the natural thing to do if you are to explain the meaning of a particular word to someone. With this, the "classical" type of definition (Definitio fit per genus proximum et differentiam specificam.), you use the copula (is, are) after the definiendum (just as if you were using an equals sign in a mathematical equation) and then go on to explain the definiendum by using the appropriate generic term plus those characteristics specific to the thing you are describing which consecutively narrow down the meaning until the definiendum can no longer be confused with anything else.
Some examples from everyday life: