Here's the whole idea in one breath: things look smaller the further away they are, and lines that are really parallel seem to lean together until they meet at a single point. Find that point, aim your lines at it, and a flat page suddenly has depth you could walk into.
Start with Something You've Already Seen
Stand on a straight road, or a train platform, and look down the tracks. The two rails are dead parallel — you know they never actually touch, or the train would be in strife. But your eyes swear blind they come together in the distance, right where the ground meets the sky. Tall things shrink, gaps close up, and everything funnels toward that one little point. Your eyes aren't lying; they're just telling you what distance does to a flat picture of the world.
For thousands of years painters couldn't quite pin this down — their buildings tilted oddly and their floors slid away at the wrong angle. Then in 1400s Florence an architect named Filippo Brunelleschi worked out the geometry of it, and suddenly artists could build rooms on a flat panel so convincing you'd reach in. That trick is linear perspective, and it's pure structural thinking: not how a place feels, but how its lines are built.
The Two Ideas That Do All the Work
The horizon is the line where land meets sky — and here's the sneaky part: it sits exactly at your eye level. Crouch down and the horizon drops with you; stand on a chair and it rises. So the horizon isn't really about the landscape at all. It's about where you're looking from.
The vanishing point is the spot on that horizon where the parallel lines appear to meet. Aim your receding lines at it and they'll behave; ignore it and your drawing will lean like a dodgy shed.
In the toy, drag the vanishing point left and right and watch every line in the scene re-aim itself at the new spot. Drag the horizon up and down and feel your own eye level rise and fall. Nothing in the world changed — only where you're standing to look at it. That's the whole secret, and now you've seen it with your own eyes.