The magnitude that mainly characterizes a magnetic dipole is the magnetic moment, which quantifies the tendency of the dipole to orient itself in a given direction in the presence of an external magnetic field.
It is a model equivalent to two rigidly connected opposite magnetic charges, in analogy with the electric dipole. It is achieved by decreasing the size of a coil traversed by an electric current, keeping its magnetic moment constant and taking the limit in which the area of the loop is zero. The magnetic dipole is the simplest case of a 2p-pole, where 2p is the number of polar pairs, which for the magnetic Gauss law is an integer.
It is a useful schematization of the influence of a magnetic field on very small coils traversed by current, and is therefore used in the context of the phenomenology of magnetism in the matter through classic atomic models (such as those of Rutherford and Bohr), through the introduction of atomic currents due to the motion of electrons and Larmor currents caused by the precession of their orbit.