This variable affects the speed and accuracy of a graph in function mode. It is how often points are selected to plot the graph. If the resolution is one, the minimum, the calculator will plot a point for every pixel in the x-direction. If resolution is the maximum, 8, the graph will plot and connect points 8 pixels apart. This creates a graph quickly, but it also creates a possibly imprecise graph.
This shows how a curve looks in both the minimum and maximum resolutions.