Sunshine50,
The sciatic nerve is a large nerve that is formed from several nerve roots, then runs out of the low back/pelvis, through the muscles in the buttocks, and down the back of the thigh.
As to where it hurts, depends upon where it is being irritated. If the nerve roots in the lower back, just as they come out of the spine, are irritated, then you will have pain in the lower back. These nerve roots come together (in the lumbar plexus) to form several major nerves, including the sciatic.
However, it is more common for the sciatic nerve to be irritated as it goes through the tight muscles in the buttocks (like the piriformis). Then because of the irritation and compression, the pain will radiate down the back of the thigh, sometimes even into the calf or foot.
Back pain is more commonly caused by problems with the muscles, discs, or facet joints. But, it is possible for the nerves in the lumbar plexus to cause pain, it is just not as common.
Good luck.