To give an example, a hexagon is a collection of 6 points in the plane. The order in which the points are taken is important. This ordering is cyclic, in that 1 comes before 2 and after 6.
The blue lines are not part of the hexagon. They are just drawn in to indicate the ordering of the points. They represent a circuit you would take if you walked from point to point in the correct order. The hexagon with the red dot in the center is convex , The others are not.

An octagon is just like a hexagon, except that there are 8 points. In general, a N-gon is a collection of N points in the plane, ordered as above. The words N-gon and polygon are synonymous.