Paths in Illustrator are open or closed, one or the other, with nothing in between. Open and closed paths differ in the following ways:
An open path has endpoints. It starts in one place and ends in another place — clearly a line segment, and not a polygon.
A closed path has no starting point and no endpoint. Like that psychotic bunny in the battery commercial, it just keeps going and going in the same place — clearly the boundary of a solid shape. (Think of complete circles, M?bius strips, and so forth.)
Creating artwork with the Pen tool is much easier if you set your fill color to None, regardless of the final color you’re going to fill your artwork with. When you use the Pen tool with a fill color selected, Illustrator treats every line you make as though it were a completed object by drawing a temporary, invisible line straight from the first anchor point in the path to the last anchor point, and then fills the enclosed area with the selected fill color. This is confusing at best because it hides parts of the path that you are creating and creates an object that appears to change shape completely with every click of the mouse. To avoid this mess, set your fill color to None while you create your path and change the fill color when the path is complete.