Faraday invented the idea of field lines as a way of reasoning about what was the case at one place around a magnet. He thought with field lines to invent electric motors, transformers and generators. Thinking with field lines is productive.
Faraday imagined field lines like special stretched elastic cords that pushed each other apart. ( Field lines are under tension along their axis, but repel other field lines at right angles to the axis).
By thinking about field lines like Faraday you can predict what magnets and magnetic materials will do in magnetic fields.