Regression analysis is a statistical method where the mean of one or more random variables is predicted conditioned on other (measured) random variables. In particular, there are linear regression, logistic regression and supervised learning.
One of the two variables, call it X, can be regarded as constant, i.e., non-random, because we can measure it without substantial error and in some cases even prescribe its values. Here X is called the independent valuable, or sometimes the controlled variable because we can control it (set it as values we choose). The other variable, Y, is a random variable, and we are interested in the dependence of Y on X.
Typically examples are the dependence of the blood pressure Y on the age X of a person or, as we shall now say, the regression of Y on X, the regression of the gain of weight Y of certain animals on the daily ration of food X.