Generally, in ray tracing, light paths are traced backward from the image plane into the scene; the digram suggests modeling the optics explicitly to capture certain effects (in this case, depth-of-field). Note the diagram uses the term "film plane" instead of image plane or screen plane, as the diagram models a camera when film use was common, before high quality CCDs were available.

In this case, interaction with the lens implies the focal point: all paths originating from the same point on the image plane will converge at the focal point (assuming the paths first intersect the lens - note the diagram does not show an aperture, which would block paths that don't) - but paths are not coincident from the lens and diverge beyond the focal point - so they intersect the scene at different locations nearer and further than the focal point. The variation in scene intersection locations, given the same origin on the image plane (and therefore contributing to the same pixel in the computed image), is what gives the depth of field effect - i.e. something looking like circular blur outside of the plane of focus. Other effects are possible here, such as anti-aliasing by varying the origin of rays across a pixel's area in the image plane.

Instead of a screen plane in front of the eye, it describes a film plane, where the image is projected, to explicitly model camera optics. You don't need to compute the focal point in doing ray tracing - it's just a way to find the plane of focus for depth of field effects.

For depth of field effects I use a standard perspective projection but jitter the position of the eye on a circle parallel to the focal plane - and I make sure all my rays for a given pixel go through the same spot on the focal plane making it sharp while stuff in front of or behind that plane ends up blurry. It's a simple model of something like an aperture, and gives pretty good results.