Often in science we are looking at 'cause' and 'effect'. You can think of the independent variable as being the 'cause' and the dependent variable as being the 'effect'. In other words, the dependent variable is the thing that changes as a result of you changing something else.
The dependent variable is the variable of which the value is measured for each and every change in the independent variable.
e.g. Dan hangs different masses on the end of a spring to see how mass effects the spring length.
The independent variable is the variable for which values are changed or selected by the investigator.
In other words, this is the thing that you deliberately change to see what effect it has.