Final answer:
The area where a magnet can exert a force is known as a magnetic field, which is the space around the magnet influenced by its magnetic properties.
Step-by-step explanation:
The area where a magnet can exert a force is called the magnetic field. This magnetic field is a region in space around the magnet where a non-contact force is experienced by a magnet or a magnetic material. It includes the space directly surrounding the magnet, between its poles, and extends to where its magnetic influence can be felt. Earth's protective magnetosphere is an example of a magnetic field that traps charged particles from space, illustrating how a magnetic field can extend beyond the atmosphere and interact with cosmic forces.