Okay, so a lot of people out there may be confused as to what exactly The Witness' gameplay hook is.
This is the first puzzle in the game, akin to teaching you how to jump in Braid
You have a pointer (little white dot) that you can move and set into a start point (the circle) on the line puzzle.
You fill the line as you move in the puzzle. You cannot cannot cross a path you've filled. There is a ping at the destination. The pointer reaches it and voila, you've solved it and the door attached to this puzzle opens.
Simply reaching the destination is not the solution of this type of puzzle. And opening doors is not the only thing a line puzzle does.
In this example, the player reaches the pinged destination but takes the wrong route.
How are you supposed to know which route is the correct one?
Now look at this puzzle:
Hard to see but you can make out the shape. Why is it shaped like that? Why are there trees around this puzzle?
... Wait. You walk up to one of the trees and notice something about the branches. You go back to the line puzzle, trace a path based on what you found out and... eureka! Now imagine a puzzle involving leaves on a tree, the design of a building, the way objects are arranged in the room you're in, or the path you just took through a hedge maze. Yeah. But wait, I can just solve these with trial and error! It may be true for some of these puzzles, but-
Now imagine multiple start points, multiple end points,information in the form of dots on the puzzle, and multiple puzzles linked together..
Now look at this:
Notice how the paths are linked together. Also notice how the paths deliberately wrap around or go between the colored dots on the puzzle. Yeah. And there's this:
The plainest example of how the a line puzzle can affect the the world: it straight up controls this mirror which directs a beam of light. Of course you don't solve it by picking the right angle alone, but the beam has to reach here in the first place.
So yeah, if you've ever played Myst, this is kind of like that: except with a cohesive element throughout: these line puzzles.
And expect a mind-blowing twist or two involving the island and/or this gameplay idea. This is Jonathan Blow we're talking about here.