For our own ease, we usually work on a 2-dimension. However, that is not reality. The reality is based on 3-dimensions (neglecting the time dimension). Then how come we are able to perform our calculations on a 2-dimension scale? With the help of planes.
What is a Plane?
Take a graph paper and draw a random graph of anything. We all know that whatever you drew, that graph will have a mathematical equation that will define it. We want you to focus on the graph paper, not on the graph. There is something where all 2-dimensional graphs are drawn. That something is called a "Plane". A plane has two dimensions: length and width. A plane will never have a height, that is a very important factor. However, one thing to note is that the graph paper will have some kind of thickness, which means it has a height. Hence, graph paper can't be a plane, we used this as an example to explain to you the concept of a plane. Furthermore, a plane runs to infinite, it has no specific length and width. It stretches to infinity and graph paper has a definite length and width, hence another reason not to call it a plane.
The above picture represents two planes, the red one 
is perpendicular to the plane, 
. Yes, planes can interact with each other too and also, planes can be in different directions. For example, the beta plane is vertical while the alpha plane is horizontal. A plane is represented by a parallelogram or a quadrilateral. The angles are named by Greek letters: (alpha), (beta) ...
Determination of a Plane
A plane can be defined in many ways. Below are the ways that can be used to determine a plane.
1. Three points that are not aligned. A point is a single dot that represents an exact location on a flat surface. It has no dimension. If we have at least three points, we can make a combination. The combination will acquire some area and that area will be of a plane. Take an example of the below figure. There are three points, and they are not aligned. Of course, they lie somewhere that proves their existence. That is why we will say that all three points lie on a plane and the plane will be named after those points, i.e. ABC plane.
2. Two lines that intersect. When two lines cut each other, there will be only one place where a flat plane can lie where both lines can be made.
3. Two parallel lines. Take an example of the below diagram. There will be a single position where a plane can rest on both lines.
4. A point and a line. Of course, a line and a point can't lie without support. There will be a plane under both, line and the point, where they both can lie.
Properties of the Plane
Planes also have properties of their own. Below are the properties of a plane:
1.A plane contains infinite points.
2.A plane contains infinite straight lines.
3.A plane is unlimited.
4.Two intersecting planes determine a line.
5.A straight line that has two points in the plane is contained in that plain.
6.A straight line passes through infinite planes.
Half-Plane
Last but not the least, a half-plane is each of the parts that a plane is divided into when intersected by a line or another plain.
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I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html