MOND is a theory developed by Israeli scientist Mordeci Milgrom about thirty years ago, that describes galaxy level phenomena usually attributed to dark matter in the form of an equation that modifies Newton's law of gravity in weak gravitational fields beyond an acceleration value that is constant in the theory.
MOND does not have an underlying theoretical basis, although it suggests possible ones. But, in its domain of applicability, at the level of systems the size of single galaxies or smaller, it explains observed phenomena parsimoniously with just one experimentally measured parameter and one formula.
MOND is not an accurate law of nature in all circumstances. It substantially underestimates dark matter phenomena in systems the size of galactic clusters or larger, and also has problems in systems such as the Bullet Cluster collision. It is also not relativistic, although a generalization of MOND called TeVeS has been developed by one of Mr. Milgrom's colleagues. But, in its domain of applicability describing kinematics in systems the size of single galaxies or smaller, general relativity and Newtonian gravity are usually assumed to be almost indistinguishable.
One of the things that makes MOND particularly notable is that it has made numerous predictions before evidence was available and without modification regarding dark matter phenomena in its domain of applicability that have later been established empirically. It has a better track record in that regard that dark matter theory.
Thus, even if dark matter effects are due to particles rather than a modification of the laws of gravity, and even if there is something wrong with MOND's modified gravity formula, it has empirically been demonstrated to be a succinct and accurate description of reality in its domain of applicability.
In other words, whatever the true mechanism of dark matter phenomena is, whether it is a "dark sector" of particles, or a modification of the laws of gravity, or a previously not understood non-linear implication of general relativity, the correct answer must reduce to something equivalent to MOND in its domain of applicability in practice.
The latest paper on the subject, demonstrates that MOND again makes accurate predictions about the frequency with which bulges are observed in spiral galaxies, which is contrary to the predictions made by standard cold dark matter theories. The paper also makes further predictions regarding these bulges which can be confirmed in future research.