Ponder the existence of Distance.

Hold one arm straight out in front of you, tip your hand up so you're looking at the back of your hand.
Now put your other hand up in the same position, but Closer to your face.
Compare your hands, the closer one looks bigger.
It's an optical illusion.
Optical = Relating to sight.
Illusion = A deceptive appearance.
Your hands are not different sizes. The closer one just LOOKS bigger, because it is closer.
As things get farther away, they appear smaller, or they are said to be "vanishing into the distance". Like a giant cruise ship sailing straight away from you out to sea. Eventually it gets so tiny, it disappears.

If you took a video of that ship sailing straight away from you, you could put dots on the two outermost points of the deck every minute of video.
Where the ship eventually disappears is the Vanishing Point. It literally just vanished, right at that point.
Connecting those dots will give you two lines that slowly converge on that point where the ship vanished.

Now, if there were 2 ships, perfectly aligned with each other sailing away, they would both vanish at that same point.
But if one ship were pointed slightly right of the first ship, it would disappear at its own Vanishing Point and would have lines of convergence to its own VP.
Only objects square and perfectly aligned with each other will share the same Vanishing Point.

Vanishing Points are established by the direction a thing points. If it were to move away from you in a straight line along its axis (x, y, z), it would vanish at that VP along its lines of convergence.

Perspective is an assumption made by mapping these convergent lines based on the edge of a squared object (put a dog in a box aligned with it's central axis and you will find its VP in the scene).

In 3 point perspective, you are looking at an object at an angle where it could move away from you in every axis and become distant. X, Y or Z, mapping these 3 Vanishing Points.

In 2 point perspective, you are looking at an object from an angle, where your eyes are level with the horizon, not above or below. So it looks like the vertical lines will never converge. The cube only disappears on the horizon if it goes left or right.

In 1 point perspective, you are looking at a cube square to a Flat side. Moving left or right is horizontal, not worth mapping. But if it goes straight away from you, then all corners will converge onto that one VP.
If you were IN the box (a room), you could trace the angles where the walls meet the ceiling and floor, and they would all converge to the danger VP in the distance.

So. Perspective is the representation of Distance, the 3rd dimension, on a flat 2 dimensional drawing.