Discrete variable - can take certain values only in a defined range , say (0,2,4,6,.....) or (.....,-10,-3,4,11,......) or numbers like that...e.g. number of cylinders in an engine can only be 1,2,3,4 etc...It can never be 1.5 or 2.5 or 3.7.....
Continuous variable - it can take any value in a range....go with the rational number property i.e. between any two rational number there will be another rational number (take average of two)....that way continuous variables can take any value in a range....e.g. mileage of a car can be anything like 9,9.3,9.7,9.994,12.35 etc
Regards