Some examples of continuous variables are measuring people's weight within a certain range, measuring the amount of gas put into a gas tank or measuring the height of people. A continuous variable is any variable that can be any value in a certain range.
The other possible type of variable is called a discrete variable. This type of variable can only be certain specific values. For example, when flipping a coin, it can land either on heads or tails. There is no in-between value like 0.5 heads and 0.5 tails. With a continuous variable, the variable can be an infinite amount of numbers between a certain reasonable range.