It seems as if there is something out there, around the magnet. We reach out with hands and touch things, so affecting them. This is a local action, affecting things nearby: physics Magnets also reach out and touch things. To make magnet's action local physicists got to invent the idea of a magnetic field. By tracking where your hands are (perhaps by proprioception), you can account for what happens right there. Fields perform a similar function: the magnet is the source of the field, but once you know what the field is at a point, you can predict what happens to magnets and magnetic materials just using what's going on locally. Fields make action without contact local action again. Move further from a magnet and the effects of the magnet are smaller. So the field is weaker. So you'd want some way of representing the field that shows where it is stronger and weaker, as well as the direction of the push or pull.
(You'd also want electric and gravity forces to be predictable by using fields—but electric and magnetic fields.)