Why do nerves cause feeling?

It's what they do: Peripheral nerves have primarily 2 functions: to send information out to the body from the brain and spinal cord, and to send information from the body back to the spinal cord and brain. Sensory nerves do the latter -- and among the types of impulses coming into the brain & spinal cord through them, is painful sensation, heat, etc. Emotional pain is an even more complex process.