The line through two points, (a, f(a)) and (a+h, f(a+h)), on f(x)=x² is a secant line. Gradually reduce h and see what the secant slope approaches.
The derivative is defined as f'(a) = lim(h→0) [f(a+h)-f(a)] / h. In other words, the limit of the average rate of change (the secant slope) as h approaches 0 is the instantaneous rate of change (the tangent slope) at that point.