A magnetic field is one of the fields, or force fields, that are known to science, to modern physics. Electric fields are another one; when an electric field builds up, it could lead to lightning between the clouds and the ground. When a magnetic field is present, if it's a weak one, like the Earth's magnetic field, it would align compasses, so that you know which way is north. As it's a stronger and stronger magnetic field, it has even stronger effects. It can hold things to your refrigerator or, in the case of our magnets, can greatly affect how electrons move inside of materials, inside of crystals.
We are sometimes asked if our magnetic fields affect cars driving by on the street and that's not a problem. The magnets are very powerful, but only in a small region of space. The magnetic fields barely reach outside of our own building, actually.