The hyperplane can be considered as the first brick to be employed when building a support vector machine.

Have you ever played with one of those tanks full of coloured solid plastic balls? Yeah, it actually is a game for children, but you should at least know what I am talking about.

OK, let's perform some mental experiments with one of those tanks. First of all, let's imagine it being filled only with red and yellow balls. We take the empty tank, we first fill half of it with the yellow ones and then with the red ones. They don't mix up since we fill the tank carefully, and in the end we should have something similar to the following:   

Let's imagine now that we take a really big blade and insert it into the tank from one side (don't worry, it is a mental experiment, you won't have to repay the tank's owner), at a height which is approximately half of the tank:

You see? The blade divides the tank into two groups. The balls on the top of the blade are the yellow balls, while on the bottom are the red ones.

Congratulations! You have just understood what a hyperplane is. We will make it more formal in a minute, but at the moment just understand that a hyperplane is some kind of plane (we will talk more about this later) able to exactly separate our data into two groups depending on the response variable we are looking at.

In a 3D space, this hyperplane is actually represented by a solid plane like our blade is, while in two dimensions it will be a line, and in more then three dimensions it will be hardly imaginable even if still formally defined.

Nevertheless, just take a second to focus on the main point of our first experiment: there is a plane that crops the tank and divides the balls into two groups based on their colours.

We are now going to make our experiment even more mental. Let's imagine that our balls start to levitate in the air. Let me show you how:

You see? They are still divided into two groups but are now placed apart from each other. Is there still a plane able to divide the balls into two groups?

For sure there is, and we can even draw it:

If we look at it carefully, we can actually see more than one possible plane. Moving the first one we drew just a bit will produce a nearly infinite number of other planes. Which is the best one?

Answering this question introduces the concept of the maximal margin classifier, which was the first classification algorithm based on a hyperplane to be introduced.