Final answer:
The nurse instructs the client to press the handheld button when the fetus moves in order to mark the fetal monitor tracing with the client's reports of fetal movements.
Step-by-step explanation:
The handheld button that the nurse instructs the client to press when the fetus moves is used to mark the fetal monitor tracing with the client's reports of fetal movements. This action allows healthcare providers to track and record the movement patterns of the fetus during labor.