A discrete quantity is a quantity that can only take specific values. An example would be the number of times a person has gone skydiving. Notice that the value of that quantity can only be specific values like If the independent variable of a function is a discrete quantity, it is said that the function has a discrete domain. Such a function can be recognized by its graph, which consists of any number of unconnected points.
Note that a discrete quantity doesn't have to be integers. For instance, if a quantity has the possible values it is discrete. In context, discrete quantities arise when working with things that can't be divided into infinitely many parts. This could for instance be how many children one has, or the number of apples purchases. These are most often restricted to whole numbers, but there are exceptions.