It is the region near a magnet that influences other magnets or ferromagnetic and paramagnetic materials such as cobalt and iron.
Compare magnetic field with gravitational field or electric field and you will see that they all have the equivalent characteristics.
It is also possible to define a vector that describes this field, called a magnetic induction vector and symbolized by . If we can place a small compass at a point under field action the vector will have direction of the straight line in which the needle aligns and direction where the magnetic north pole of the needle points.
If we can trace all the points where there is an associated magnetic induction vector we will see lines that are called magnetic field induction lines. they are oriented from the north pole to the south, and at each point the vector tangency to these lines.
Induction lines also exist inside the magnet, so they are closed lines and their internal orientation is from the south pole to the north pole. Like power lines, induction lines cannot intersect and are denser where the field is most intense.