independent and dependent variables

Distinguishing variables of a function:

Let $y=f(x)$, where $f:x\mapsto y$.
Since $y$ is determined via $f$ by $x$ (as $f$ is a function of the variable $x$), we say $y$ is the dependent variable, since finding a value for $y$ requires a value of $x$, i.e. $y$ "depends on" $x$.
Since $x$ does not depend on any other variables, we say it is an independent variable.

In contextual applications, the independent variable is often a known or discoverable/measurable quantity, while the dependent variable is unknown or desired to be predicted.