A "discrete variable” is the one which takes only isolated or discontinuous values. There are jumps in case of a discrete variable, e.g., number of goals scored in a match. Intermediate values between 1 and 2 or between 2 and 3 are not possible as there cannot be 1.4 or 2.5 goals in a match. Similarly, the number of children in a family, number of students in a class, fans produced in a factory in a particular year etc. are examples of discrete variables.
Whereas a continuous variable is the one which can take any value in a specified interval. Temperature recorded of patients in a hospital, heights of all BBA students of a University, wages of all workers in a factory are some examples of continuous variables.