For now just think of a discrete set as one in which the elements are separated from one another. Discrete mathematics is useful in a wide variety of disciplines. Civil engineers deal with discrete sets of objects to design and construct bridges and other structures. Computer scientists use discrete sets to represent data storage, languages and networks. Electrical engineers manipulate the elements in discrete sets to construct circuits and hardware systems.
Physicists consider discrete sets of atoms but also study discrete sets of celestial bodies.
Biologists examine the behavior of discrete sets of individuals in a population. Discrete mathematics is the common thread.