How do epidurals work to ease pain in labor?

Nerve block. Epidurals block the nerves to the pelvis with an infusion of local anesthetic around the spinal cord. This blocks the pain signals from reaching the brain, thus eliminating the sensation of pain. A good epidural will block pain while preserving some motor function. A very dense epidural will completely eliminate pain, but will interfere with leg function to a greater degree.
Meds numb nerves. A small catheter is inserted into an area of the spine called the epidural space. Medication goes through the catheter and soaks the nerves in that area. As the nerves are exposed to the medication you lose sensation and experience pain relief. The medication can be given continuously until you deliver to keep you comfortable.
Epidurals work. By bathing the nerve roots that cause labor pains with local anesthetic, causing loss of sensation and numbness. Because of the area where the medicines are administered, the numbness is much more controlled than in a spinal, which is why you don't feel pain, but can still move your legs and push when it is time to deliver the baby.