How serious or dangerous is a herniated disk?

Depends: It depends on size, location, and how large your spinal canal (channel where the nerves and spinal cord are). If it pushes on your spinal cord and affects its function, it is potentially very serious. If it pushes on a nerve and there is enough irritation to lose strength and feeling that is progressive or severe, it is also a problem. Most herniations are not this serious, improving with time.

Usually not dangerou: Most herniated discs are self limiting & get better with 10% going on to surgery. Most are not serious or dangerous with only 1% leading to a condition related to bowel/bladder control issues known as a cauda equina syndrome that requires emergent surgery. Occasionally, disc herniations in the thoracic & cervical regions can lead to spinal cord compression or myleopathy that also needs surgery.