The "Number of Copies" is the number of cross-sections of the original object that will be created through the entire length of the sweep.
For example, if you set the "Number of Copies" to 36 and sweep once around the axis (360 degrees) you will ge a cross section at every 360/36 = 10 degrees. In my experience this is just about the minimum angle between sections that will render smoothly at all zoom levels.
If you aren't going to zoom in too closely you can get by with 16 or 18 copies per sweep around the axis. At high zoom levels and some angles the surface will be rendered smoothly but the edges will be jagged.
This also applies to cylinders and other solid objects. I often use 12 sections for small details that will never be viewed closely, like small bolts. I use 8 sections for cables that won't be viewed closely. These always render as octagonal, and from a distance they look like multi-strand cables.
If you do three complete turns about the sweep axis the angle between sections will be 3x360/N where N = the "Number of Copies." If N = 10 and you have three sweeps (1080 degrees) the angle between sections will be 108 degrees. This is so great that the shading algorithm treats the surfaces between sections as flat with sharp edges and the surface does not render smoothly. For three turns you need at least 3x36 = 108 sections to get a smoothly rendered surface.
The algorithm tries to figure out what it is you have created, and what it should look like. There is a maximum angle between sections for smooth surfaces. Beyond that the program decides that you have created something with flat surfaces and doesn't try to create smooth shadings. For example, it always renders surfaces at 90 degree angles to each other as flat surfaces that come together at a sharp edge.
The more copies you use the larger the file size, and the longer it takes to render. I once created a simple tubular hand railing up inclined steps using the default settings and it came out to be 13 Mbytes! I then redid it with 36 facet cylinders and 18 sections per 90 degree sweep and it was about 10 Kbytes. Both rendered to look exactly alike.