Regression that includes two or more non-constant independent variables. Also known as multivariable regression.
For two or more dependent variables, use multivariate-regression.
Linear regression models a variable (the "dependent variable") as varying randomly with respect to a linear combination of other variables (the "independent variables"). Multiple regression includes two or more non-constant independent variables (whence, three or more variables in toto). This adds complications not present with only one independent variable, including complex forms of correlation and interaction effects.
multiple-regression tag instead of the more generic regression tag when your question focuses on an issue specifically related to including two or more independent variables in a regression model.
Multiple regression concerns the so-called "general linear model," not to be confused with the generalized linear model despite the close similarity of their names.