What it is:
A runs test is a statistical procedure that can be used to decide if a data set is being generated randomly, or if there is some underlying variable that is driving results.
How it works/Example:
If data points are randomly distributed above and below a regression curve, you should be able to predict the number of patterns (runs) you'd expect to see. If there are more patterns than you would expect statistically, there must be some relationship among the variables that is contributing to the abnormally high number of runs.
Why it matters:
Randomness is one of the key assumptions in determining if a univariate (only one variable) statistical process is in control. If you can't determine that an outcome of a trial is random, then you have to adjust your statistical methods accordingly.