An explanatory variable is one variable in a pair of variables which we suspect affects the other. Labeling a variable as explanatory of another variable does not guarantee the relationship between the two is actually causal. It is merely a label so we can keep track of which variables we suspect affects the other.
In a pair of variables, where one is an explanatory variable, the other is the response variable.
One could say that an explanatory variable might affect a response variable.