Understanding open and closed paths

Paths are either open or closed:

An open path has a beginning point and an ending point that do not connect.
A closed path's beginning point and ending point are the same point.
Open path and closed path
 
A single path can overlap itself to create a loop that appears to enclose an area, but that is not a closed path. Only joined endpoints create a closed path.

Either type of path can have a fill. For more about fills, see Changing the fill of the drawing tools.