A computer can not draw a curved line or a circle. A path, in Adobe Photoshop or Adobe Illustrator, is actually a Bézier (beh-zee-ay) Curve. The Bézier curve is named after French engineer Pierre Bézier. A Bézier curve is a series of straight lines, set at angles, that make the shape of the lines go in the direction of the curve. The more points (vertices) in the line, the more tiny lines make up the curve. Now, we don't see these vertices. We just see the path itself, along with the anchor points and their control arms. If you were to graph out the points of the curved path, you would see all of the straight lines that comprise the path.
Paths - Outlines - Bézier Curves
Precision Retouching
Precision retouching requires precision path work. Defining edge pixels, illustrating and modeling elements, compositing, and creating complex masks, are all best done with outlines. We never create outlines from selections, but we do create selections from outlines. And of course, there's the obvious use of Clipping Paths.
Tid-bit: Back before page layout programs auto selected paths to be Clipping Paths, we had to manually define them, and set its tolerance. The tolerance told the RIP how many vertices the path should have. Try to output a path with too many vertices, and down went the RIP.