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The end goal is to take a 3D model of a teapot as input, and produce a 2D picture of a teapot as output. The 3D model is essentially a collection of points on the teapot's surface. The output image is a 2D grid of pixels, each having a color value.
The idea is that when we look at an object, our eye detects rays of light bouncing off the object. Some rays hit our eye towards the left-hand side of the detection zone; some hit the lower-right-hand side; etc, etc. And we're able to "understand" this flood of rays as a 2D image, and "see" it in our mind. Or something like that.
This program works similarly to the above description. Each pixel in the output image corresponds to a tiny part of the eye (the images above have 64x48 pixels, so we're modelling the eye as having 64x48=3072 "parts"). Each pixel (part) is assigned a color value, based on the color and amount of light hitting it.
As you can see above, we haven't rendered a teapot yet, but it's been fun regardless! I've been following matklad's Ray Tracer Construction Kit, which I highly recommend.