The question is not vague. The man has a set of n (x,y) coordinates that he wants to plot a polynomial of the nth order through.
Let's say our polynomial looks like this:
y = a0 + a1 x + a2 x2 + a3 x3 + ... + an xn
If we fill in the (x,y) pairs in this equation, we get n equations and since we have n unknowns (a0 .. an) we can solve the equations. This is usually done in matrix form.