The medical branch nerves supply the facet joints and send the pain signal from those joints to the brain. They also support the main muscles in your back.
Median branch nerve block deliver local anesthetic on top of those nerves, as a diagnostic tool (test) to see if your pain improves. You will be asked to keep track of the percentage and duration of relief afterward. If it works, it is often repeated to rule put placebo effect (sugar pill effect) i.e. ruling out you felt better, just because you had an injection. If it works twice, then you are likely a candidate for Radiofrequency Rhizotomy.