A magnet produces a vector field, the magnetic field, at all points in the space around it. It can be defined by measuring the force the field exerts on a moving charged particle, such as an electron.
Magnetic field lines
A magnetic field line can be thought of as consisting of lines of force. The forces of magnetic attraction and repulsion move along the lines of force.
Magnetic pole models
Geomagnetic models form the foundation of traditional, compass-based navigational systems. 
The primary world model is the International Geomagnetic Reference Field (IGRF), compiled from magnetic measurements 
collected by national observatories in many countries, as well as readings made from ships, airplanes, and satellites.
1- Magnetic pole model and the H-field
2- Amperian loop model and the B-field
Amperian loop model
Electric currents produce a magnetic field and Ampere discovered that electric currents attracted and repelled each other similar to magnets, it was natural to hypothesize that all magnetic fields are due to electric current loops.

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