The text seemed to describe it quite well. They just use a bunch of physics jargon because the book approaches rendering from the physics side of things.

Light leaving a point in a direction = light emitted from that point in that direction (zero if we aren't talking about a light bulb or something) plus all light reflected by that point in that direction.

As a mathematician by training who does a lot of programming for a living: This is the biggest misconception about math I see coming from programmers. There's frequently a complaint about notation (be it that it is too compact, too obscure, too gatekept, whatever) and the difficulty in picking out what a given "line" (meaning equation or diagram or theorem, or whatever) means without context.

Here's the thing though: Mathematics isn't code! The symbols we use to form, say, equations, are not the "code" of a paper or a proof. Unless you yourself are an expert at the domain covered by the paper, you're unlikely to be able to piece together what the paper wants to convey from the equations alone. That's because mathematics is written down by humans for humans, and is almost always conveyed as prose, and the equations (or diagrams or whatever) are merely part of that text. It is way easier to read source code for a computer program because, by definition, that is all the computer has to work with. The recipient of a mathematical text is a human with mathematical training and experience.

Don't interpret this as gatekeeping. Just as a hint that math isn't code, and is not intended to be code (barring math written as actual code for proof assistants, of course, but that's a tiny minority).

Screenshot and ask ChatGPT. Works pretty well.