Linear regression is a process in statistical mathematics. It gives a numerical measure of the strength of a relationship between variables, one of which, the independent variable, is assumed to have an association with the other, the dependent variable. Note that this relationship is not assumed to be one of cause and effect -- although it can be -- but simply one of correlation.
Say you have a list of runners on a track team, along with their individual training logs and 5K run times. You can assume that the number of miles they run in training, M, influences their 5K performance, T. With M as the independent variable and T as the dependent variable, you can plot a graph of T vs. M and use this graph as a visual estimation as to whether a relationship exists.
The Regression Line
As with any straight line, a regression line takes the form y = ax + b, in which y is the dependent variable, a is the slope of the line, x is the independent variable and b is the point on the y-axis at which the line crosses it.