Imagine you have a big toy plane and a small toy person standing outside the plane. The toy person wants to know how far away they are from the toy plane.
They can do this by measuring the straight line distance from themselves to the closest point on the toy plane. Think of it like drawing a line down from the toy person to the toy plane. The point where the line touches the toy plane is the closest point.
This distance is called the "distance from a point to a plane". It's just the distance between the toy person and the closest point on the toy plane. The toy person could use a ruler or a measuring tape to figure out exactly how far away they are from the plane.
In real life, people use this concept to talk about how far away things are. For example, if you're flying in a plane and you look out the window, you might see mountains or buildings below. You can measure the distance from the plane to the ground using the same idea - you measure the straight line distance from the plane to the closest point on the ground.