In statistics, a variable is any quantity that is a part of a data point. Variables can either be dependent or independent. An independent variable is a quantity that is directly controlled by the observer or experimenter. The dependent variable, as its name suggests, depends on the independent variable. The dependent variable is often the quantity you want to measure, and it the result of the experiment or test.
For example, you may want to determine the relationship between hemoglobin concentration and age. You select people of various ages, and then test their hemoglobin concentrations. Age is the independent variable, and is controlled by the experimenter (you can select which ages are in the experiment). The dependent variable is the resulting hemoglobin concentration.
In some cases, these criteria may not be useful in determining which variable should be the independent variable, such as determining the correlation between the readings given by two different instruments for the same samples. In that case, there might be other criteria for selecting the independent variable.
