Whiplash or flexion/extension injury is a soft tissue injury to the neck. Whiplash is also called neck sprain or neck strain. Symptoms may occur right after the injury or they can be delayed by several days, just as you've described.
Pain occurs because of the sudden movement forward (flexion) and then back (extension). Neck stiffness, headaches, and dizziness are common. Some people also have upper back, shoulder, and arm pain with numbness and tingling down the arm.
Exactly which structures are injured is not really known. It's likely that the ligaments or muscles are stretched and torn between the vertebrae. There may be some small areas of bruising and swelling within the spinal cord itself. Symptoms are delayed until enough swelling and inflammation occur to press on sensitive nerve endings. This can take anywhere from 24 to 48 hours.