The equation of a circle is:
r2 = ( x - a)2 + ( y - b)2
where the points (a, b) are the centre of the circle and r is the radius of the circle.
Hough's Transform can be generalised to detect a group of points lying on any sort of a curve. The complexity increases very rapidly with the number of parameters needed to define the curve.
Although it is a little bit more complex for a circle, as you are dealing with 3 planes, x, y, and z, as opposed to 2 planes the principle is the same. Again you take a number of points from the circle and put them through this transform. The result is a complete circle without the background noise.
The benefit of this is for tracking the pupil of the eye. You must remember that Mathematics assumes everything is perfect . Engineers uses Mathematics to help them model the real world which itself is not always perfect. So when trying to get segmentations of the eye which is circular but not quite, they use Hough's Transform to create the image suitable to work with.