Piper accidentally cuts her finger while chopping vegetables. why does she feel pain?

Her nerves send signals of pain to her nervous system and back to her finger and then she feels the pain.

When piper cuts her finger, sensory neurons in her fingers detect the stimuli (knife to cut the vegetables) and, through a nerve impulse, send this information through connector neurons in the peripheral nervous system to the central nervous system - and eventually to the brain. The information is then processed and then another nerve impulse is sent from her brain to her body so that she can react and respond to cutting her finger (which likely is to move away from the knife). Hope this helps a little.