Consider that we place the the magnetometer in the central axis of the carousel. In this imaginary carousel, there is a child that has in one pocket an electrically charged ball and in the other a bar magnet. From time to time, the child gets bored from its place in the carousel and goes to another place, sometimes it even tries to go up to the center of the carousel.

In this picture, the child represents an electron, that has two properties, corresponding to things in the child’s pockets, it’s charge, i.e., the electrically charged ball and its spin, i.e., the bar magnet. The magnetometer stands for the nucleus.
When the child is in a spot of the carousel, it is orbiting the magnetometer in the central axis of the carousel, the latter will measure a magnetic field that is due to both the bar magnet in the child’s pocket and to the orbiting of the electrically charged ball in the other pocket, i.e., the dipolar and orbital hyperfine contributions. But as the electrons, the child is not in the same place all the time, so the reading in the magnetometer will change over time but tend to an average value. When the child goes up to the center axis, will have a “contact” contribution in the magnetometer, representing the Fermi-contact term.