second order accuracy in PDE

Question

When I read finite difference method I encountered the below formula which is used to approximate the second order PDE: $$ \frac{d^{2}u(x)}{dx^{2}} = \frac{u(x+h)-2u(x)+u(x-h)}{h^2}- \frac{h^2}{12}\frac{d^4u(\xi)}{dx^4} \quad \quad \text{where} \xi_- \leq \xi \leq \xi_+ $$ The formula gives an approximation of $\frac{d^{2}u(x)}{dx^{2}}$ with a second order accuracy $O(h^2)$. What does this second order accuracy mean in practice (assuming I know value of h)?