What is a polygon?

A polygon is a two-dimensional (plane) shape. A polygon has straight sides, thus a circle is not a polygon because it has curved sides.
A polygon has a minimum of 3 sides. A polygon must be closed; if the sides do not fully connect it cannot be a polygon. If the shape is open, it is not a polygon.
The number of sides that a polygon has relates to its name. For example: a triangle has 3 sides, quadrilateral 4 sides, pentagon 5 sides, etc.
A polygon that has all sides and angles the same is called a regular polygon. For example, a square is a regular polygon, or regular quadrilateral, because it has 4 equal sides and 4 right angles. Some triangles are regular polygons (equilateral triangles).

A polygon is a closed figure made up of straight line segments.
A triangle is an example of a polygon. It is made up of three straight line segments that meet at three points, or vertices (the point where the sides of a polygon meet), to form the closed shape.
Other examples include quadrilaterals (a 4 sided polygon, like a rectangle), pentagons (a 5 sided polygon), and hexagons (a 6 sided polygon).
Whereas a circle, , is not a polygon. A circle is not made up of straight line segments.
A polygon can be any shape, or be made up of any number of line segments or edges, as long as the figure or shape is closed, where all the edges meet to form a points or vertices.

A polygon is a closed figure made up of straight line segments.
grad A triangle is an example of a polygon. It is made up of three straight line segments that meet at three points, or vertices (the point where the sides of a polygon meet), to form the closed shape.
Other examples include quadrilaterals (a 4 sided polygon, like a rectangle), pentagons (a 5 sided polygon), and hexagons (a 6 sided polygon).
Whereas a circle, @, is not a polygon. A circle is not made up of straight line segments.
A polygon can be any shape, or be made up of any number of line segments or edges, as long as the figure or shape is closed, where all the edges meet to form a points or vertices.

A polygon is also considered "closed". As in, the letters "M" or "K" wouldn't be considered polygons. They aren't considered closed, unlike the letters "O" and "D". "O" and "D" have a specific inside and outside to them. One might be able to specify that "M" and "K" have an inside and outside, also. But, there isn't any "drawn" border to them already. Or, in an effort to bring some reality to this, an outline of your house could be considered a polygon, as long as your front door is closed on the drawing. Then, the figure would be closed. But, if the figure has an "open" from door, it is no longer a polygon.

What is a polygon? A lost parrot.
Seriously, there is not an agreed definition of a polygon, the primary difference being whether the interior is included or not. Polygon translates as many angles.
A typical definition of a polygon is a geometric shape created by line segments (by definition these are straight, so no "curves" are allowed). The segments meet at vertices such that:
(1) No line segments intersect, except at a vertex (sides are not self-intersecting)(2) At each vertex, exactly two line segments meet (no segment ends in a bare vertex)(3) No three vertices are collinear
See the attached pictures for examples of polygons and non-polygons.
Polygons can be convex, concave, or star. We typically study convex polygons. Here are some ways to determine if a polygon is convex or not:
(1) In a convex polygon, if you extend any of the sides, no points on these lines will be in the interior of the polygon.(2) If a convex polygon, you can choose any two points in the interior of the polygon, and every point on the segment defined by these points is in the interior of the polygon.
Regular polygons are equilateral (all sides the same length) and equiangular (all angles have the same measure).
http://mathworld.wolfram.com/Polygon.html