What is the significance of the following equation in computer vision?
I would agree - energy minimization for snakes (active contours).

It minimizes second derivative - bending of the curve.

Minimizes the difference between the image (probably it's edges) and contour (at discreet contour points - the reason for having Dirac impulse in the expression).

Usually one could expect also to have minimization of the first derivative - stretching of the snake.

More details and references on wiki - active contour