One can answer this question slightly differently depending on context. I will point out two:
(1) Scientific experimentation. In experiments, the notion of a dependent and independent variables if absolutely critical. An independent variable is one that the scientist can choose (vary) and controls. A dependent variable is one that is being measured (determined). Its value distribution depends on the control variable in some (usually non-trivial) way. So in short: independent variable is controlled, dependent is measured. An example: experiment examining a healing effect of a medication: controlled (independent) variable is the dose (0mg, 10mg, 20mg, etc), dependent variable is the outcome "healed," "not healed."
(2) mathematical functions: dependent variables are typically in the body of the functional expression and can be varies over a "domain." Dependent variable(s) is the function value that depends of the independent variable and is forced to vary within the function range. This kind of dependence is related to (1), in a mathematical sense.
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