A constant is a value that remains unchanged, such as $\displaystyle \pi$ or $\displaystyle e$ or 1. A variable is something whose value is allowed to change within a domain of values. For example, consider the formula for the area of a circle:
$\displaystyle A=\pi r^2$
$\displaystyle A$ is a variable representing the area of the circle, and in this context it is a dependent variable, because its value depends on the value of $\displaystyle r$, the radius of the circle. $\displaystyle r$ is an independent variable, as we can let it be anything we want that represents the radius of a circle, generally taken to be some positive real number, i.e. $\displaystyle 0<r$.