This is part of code for printing the description of doors. It goes with this line earlier in that section:
The initial appearance of a door is usually "Nearby [an item described] leads [item described direction]."
So, let’s say the player is in the Antechamber and they could go west through a wooden door into the Chamber. The game will print the initial appearance of the wooden door in the room description. For this, the “item described” is the wooden door. So to evaluate “[the item described direction]” we need to evaluate the first code block you quoted, with the argument “item” set to this item described (the wooden door).
Now the first two lines of that code block set “the place” (a temporary variable) to the other side of the wooden door, that is The Chamber. Then, regardless of which branch of the “if” we go through, we have to evaluate “way through the item,” which calls the second code block with the argument “threshold” set to the item, which was set to the wooden door.
The second code block now does this:
“far side” gets set to the other side of the wooden door, which is the Chamber;
way gets set to “the best route” from the location (the Antechamber, where the player is) to the Chamber, using even locked doors, which is west;
since west is a direction, the function call returns west.
This all is basically a way of asking “Which direction is the door we’re talking about from the room the player is in?”
OK, back to the first code block. There’s a test here for if “the place” (the Chamber) is visited, which is a built-in property that determines whether the player has been there. If the Chamber has been visited, it says “[way through the item] to [the place in lower case]” which is “west to the chamber”. If not, it just says “[way through the item]” which is west.
So, basically, this means that the room description will say “Nearby a wooden door leads west” if you haven’t been to the chamber, and “Nearby a wooden door leads west to the chamber” if you have been to the chamber and so what’s there. And it automates this for every door. So you don’t need this if you aren’t trying to automate the descriptions of doors in this way.
BTW, there are a couple of things here that I think may have been necessary for older versions of Inform, or that I wouldn’t do (like I know how to code Inform better than Emily Short, ha). One thing is that the first code block is something that applies only to doors, since “other side” is a property that only makes sense for doors. So I’d change “(item - a thing)” to “(item - a door)” to make sure I don’t try to invoke this with something that isn’t a door. Also, I don’t think “let place be a random room” is necessary; it should be possible to use the next line to set the place directly to the other side of the item.