What does the eigenvalue tell us?

Question

Given an grayscale image and a position $(x,y)$ at which i've calculated the Hessian $H(x,y) = \left( \begin{matrix}I_{xx} & I_{xy} \\ I_{xy} & I_{yy} \end{matrix} \right)$, where the $I_{xx/xy/yy}$ are the second order derivatives of the image $I$ in the direction $xx$, $xy$ and $yy$. I know that the eigenvector of $H$ corresponding to the largest eigenvalue indicates the direction of greatest curvature. But what does the eigenvalue itself tell us? The larger it is the larger is the curvature at this point? Or does the value itself not matter?