When investigating relationships in bivariate data, the explanatory variable is the variable that may explain or cause a difference in the response variable.
For example, when investigating the relationship between the temperature of a loaf of bread and the time it has spent in a hot oven, temperature is the response variable and time is the explanatory variable.
With numerical bivariate data it is common to attempt to model such relationships with a mathematic equation and to call the response variable the dependent variable and the explanatory variable the independent variable.
When graphing numerical data, the convention is to display the response (dependent) variable on the vertical axis and the explanatory (independent) variable on the horizontal axis.
When there is no clear causal link between the events, the classification of the variables as either the dependent or independent variable is quite arbitrary.