Paths are curves (known as Bézier-curves). In GIMP it's very easy to learn and to use them. To understand their concepts and mechanism you can go to the glossary Bézier-curve or to Wikipedia http://en.wikipedia.org/wiki/Bézier_curve. It is a very powerful tool to design sophisticated forms. To use it in GIMP you must operate by two successive ways: 1st Create the path and 2nd Stroke path.
According to the terminology used in GIMP, “Stroke path” means here to apply a specific style to the path (color, width, pattern... ).
At this step you can design a skeleton of wished form; this skeleton will be modified later by various ways. To do this you can go to Paths. A short example will be useful to understand the creating process. In menu click → in image window
or on the relevant icon in toolbox
or use hotkey B
Your pointer changes into a pen feature with a curve beginning; if you right-click in the image you print a point (white inner circle whith a black border); moving mouse and right-clicking again you create automatically a second point linked to previous one. You can carry on as often as you wish it to design a polyline, but to learn you need two points only. Now if you approach pointer close to segment ranging between the two points, the little “+” close to pointer changes into a cross (for moving). Now press down right button moving pointer to any side.
Then two events occur: one is a bending of the segment to moving direction and this bending is proportional with displacement, and the second reveals at the two curve ends two segments ended with squares (named handles). If you drop prompt on these squares this one changes into a pointing finger. Now if you are pressing down right button and are moving your mouse you can see consequence on the curve feature. By this mean you can change starting curve orientation as well as its “lenghthening” on modified side.