A discrete variable may have only specific values within a discrete set of values. You may have as example the set of integer numbers. The values the variable may take on are only integer numbers and not the values between( between -1 and 1, the variable may take only the zero value, the rest being excluded).
The continuous variables have no restraints in taking values within an interval of values and they are good to describe the temperature, the weight and the time.
A continuous variable can be of any value or number between two specific values or numbers. For example, if you lined up all the students in a classroom to see how many students were between 4 feet 6 inches tall and 6 feet 4 inches tall, you would have a set of continuous variables. A student height can take any value, as long as it is between the shortest height and the tallest height specified.
A discrete variable takes a value from a small or finite set of conditions or states. The die from a board game is one example of a discrete variable. Dice have a finite set of only four numbers: 1, 2, 3, 4, 5, and 6. There cannot be a side with 4.5 dots.