The question is not vague. The man has a set of n (x,y) coordinates that he wants to plot a polynomial of the n^th order through.

Let's say our polynomial looks like this:
y = a₀ + a₁ x + a₂ x² + a₃ x³ + ... + a_n xⁿ

If we fill in the (x,y) pairs in this equation, we get n equations and since we have n unknowns (a₀ .. a_n) we can solve the equations. This is usually done in matrix form.