What exactly is sciatic nerve pain?

Pain down the leg. The sciatic nerve is a bundle of nerve fibers that emerge from the lower spine providing wiring for the leg. If the nerve is injured or "pinched" as it exits the spine (or for that matter anywhere along it's course), the brain receives signals of pain which it may interpret as coming from somewhere along the course of the nerve. That pain is called sciatica.
Back & Leg Pain. Sciatica is pain in the distribution of the leg as a result of an irritated nerve or facet joints or other injury typically in the lumbar spine (low back) which are caused by herniated disks, spinal stenosis or degenerative disc disease, etc requiring further evaluation by a spine specialist and may be candidate for facet injections/radiofrequency ablation and epidural steroid injection.
Leg pain. Buttocks pain that radiates to calf and foot with or without foot numbness and tinglingmost frequently from disc herniation.