What does rise represent and what does run represent?

Rise represents the change in y-values on a graph, e.g. if the rise is equal to 10, the y-value changes by 10.

Run represents the change in x-values on a graph, e.g. if the run is equal to 5, the x-value changes by 5.

knowing both the rise and the run is necessary to calculate the gradient, or slope of a graph - this is done by dividing the rise by the run, in this case it would be equal to 10/5 = 2