This idea only matters for specific nuclei that have a spin number greater than one half. These specific nuclei have a non-spherical charge distribution. This means their electric charge is shaped more like a football than a perfect sphere.
The coupling constant depends on two important pieces of information. The first piece is the nuclear quadrupole moment, which describes the nuclear shape. The second piece is the electric field gradient created by nearby electrons and atoms.
This gradient is just the change in the electric field across the space of the nucleus. The coupling constant shows up in nuclear quadrupole resonance spectroscopy. It also changes the signal shapes in standard nuclear magnetic resonance spectroscopy.
These changes give chemists highly detailed clues about chemical bonding. The size of the coupling constant reveals how unbalanced the surrounding charge is. A larger number means the nearby electric field is very uneven.
The sizes of these constants vary widely between different types of elements. Deuterium has a tiny quadrupole moment and a very small coupling constant. Elements like chlorine or nitrogen have much larger coupling constants in the megahertz range. Students often forget that perfectly round nuclei feel no quadrupole coupling at all.