Understanding Regression Coefficients

In a multiple regression analysis, we seek to understand the relationship between one dependent variable and multiple independent variables. Each independent variable is associated with a coefficient that indicates how much the dependent variable is expected to increase (or decrease) when that independent variable increases by one unit, holding all other independent variables constant.

Consider a regression model where the dependent variable is Y and the independent variable is X. If the regression coefficient for X is 3, what does this imply?