Scanned image of an eye with grid lines superimposed for iris and pupil recognition from US Patent 5,291,560 by John Daugman.
A camera scans the person's eye and produces a digital image.
Image processing software attempts to isolate the iris by drawing two circles, one at its inner boundary (between the pupil and the iris) and the other at its outer boundary (known as the limbus, between the iris and the white, outer sclera). The inner boundary is relatively easy to detect, because it's generally a circle with a sudden change in brightness where the pupil gives way to the iris. A broadly similar process is used to find the outer boundary, though it has to allow for the likelihood of the eyelids blocking part of the iris.
Polar coordinates (concentric circles and radial lines from their origin) are then added to the image to define separate "zones of analysis," so that key features of the iris can be accurately located and compared in two-dimensional space. This system cleverly allows for the way the iris changes as the pupil grows (dilates) and shrinks (constricts) in different light conditions.
The pattern of light and dark areas in the iris is then converted into digital form using bandpass filters (crudely speaking, if the brightness in a given area is more than a certain amount, the filters might register a 1, otherwise they would register a 0), and, with a bit of mathematical juggling, this generates the unique, digital IrisCode®. A particular eye will generate roughly the same code whether its pupil is dilated or not.