This relates to the minor axis and the change in degree of the ellipse. Contour curves are basically the same as ellipses in that they have a degree and minor axis, the only difference is that they're just a partially drawn ellipse

In the case where the contours change direction, then the contour that we are looking dead onto would be a straight line or an ellipse with a very small, sharp degree, before widening out as they curve away from us. You might like to read over these notes again as a refresher on how this works. The example with the coin is particularly pertinent here as well.

Hopefully that makes sense. :)