Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.
"Regression" is a general term for a wide variety of techniques to analyze the relationship between one (or more) dependent variables and independent variables. Typically the dependent variables are modeled with probability distributions whose parameters are assumed to vary (deterministically) with the independent variables.
Ordinary least squares (OLS) regression affords a simple example in which the expectation of one dependent variable is assumed to depend linearly on the independent variables. The unknown coefficients in the assumed linear function are estimated by choosing values for them that minimize the sum of squared differences between the values of the dependent variable and the corresponding fitted values.