The amount that a line "runs" between two points on a line. This is, specifically, the change in the x value between the two points (delta x).
If our line includes points (2,4) and (12,17), our run is 12-2=10. 2-12=(-10) also works, but it usually makes more sense to subtract the smaller number from the larger (to get a positive value). Note: if you calculate run by doing x1-x2, don't calculate rise by doing y2-y1.
Run is used in the calculation of slope.