It's demonstrating how to find the line that passes through two points x=a, x=b on the function y=f(x).

Without having read the actual page, I assume he's going to move a and b close to eachother to approximate the tangent of the function at a point.

edit: In higher level math, you use circles/spheres or parabolas/paraboloids to approximate functions, but in high school level calculus you stick to using a straight line to approximate a function