A dependent variable is the variable that will change in an experiment. It depends on some change in other variables in the experiment. For example, if you want to know how much light a plant needs to grow, the amount of growth is the dependent. If you wanted to see if a plant would grow better in hot or cold areas your dependant variable would be the temperature of the area the plant is left in.
In calculus, a function is a map whose action is specified on variables. Take x and y to be two variables. A function f may map x to some expression in x. Assigning gives a relation between y and x. If there is some relation specifying y in terms of x, then y is known as a dependent variable (and x is an independent variable).
A dependent variable is also known as a "response variable", "regressand", "measured variable", "responding variable", "explained variable", "outcome variable", "experimental variable", and "output variable".
If the independent variable is referred to as an "explanatory variable" then the term "response variable" is preferred by some authors for the dependent variable.