Planarity is like a game of drawing where we want all the lines to be connected without crossing over each other.
Imagine you have a big piece of paper and you want to draw some objects on it. However, you have to make sure that none of the lines you draw cross over each other. This means that if you draw the outline of a shape, like a circle, you can't draw any lines inside of it that cut through the middle. They have to stay on the outside.
This is what planarity means: being able to draw lines or shapes without having any of them cross over each other. It's like trying to make sure your drawing looks neat and organized, instead of a messy scribble that's hard to understand.
In math, planarity is important because it helps us understand how different shapes and objects are related to each other. We can use it to solve problems and figure out how things should look in different situations.