Modified Newtonian Dynamics attempts to resolve the problem that when astronomers observe galaxies and apply the current theory of gravity, the results show that the stars within the galaxy should go spinning apart from each other. There is clearly something that the theory is not taking into account and, according to Modified Newtonian Dynamics, the error lies in the way the force of gravity is calculated at very long distances. By making the force and acceleration relationship, normally F = ma, into a non-linear relationship at low values of a, Modified Newtonian Dynamics claims to resolve the problem.
Most astrophysicists and cosmologists do not believe that Modified Newtonian Dynamics fits the evidence. By an overwhelming majority, the community researching such things support the theory of dark matter. As such, Modified Newtonian Dynamics falls in the informal category of a "fringe theory." Specifically, it falls in the somewhat less-informal category of an "alternative gravity theory," because it proposes fundamental changes to our understanding of the way gravity works (as opposed to dark matter theory, which supposes that our understanding of gravity is fine, but we're missing some physical substance that needs to be included in the calculations).