MOND is a theory concerning the Dark Matter problem. The problem is that our observations of certain systems are inconsistent with Newtonian dynamics. We measure less mass than Newton’s law predicts there should be. There are 2 ways of looking at this problems, the most popular is to presume that Newton’s law is correct and thus there should be mass we can’t observe (Dark Matter). The other option is to presume that our measurements are correct and that Newton’s law doesn’t predict the mass of systems with low accelarations well (the MOND theory). In this theory Newton’s law and thus some other laws are adapted to better predict the mass in these low acceleration systems.
The basis of MOND consists of 2 observed facts about spiral galaxies. 1) The rotation curves of spiral galaxies are asymptotically flat (Shostak 1973, Roberts & Whitehurst 1975, Bosma 1978, Rubin et al. 1980) and 2) there is a well-defined relation between the rotation velocity and the luminosity of such spiral galaxies, the Tully-Fisher law (Tully & Fisher 1977, Aaronson et al. 1982). So the first idea is that there should be a modification to the lengthscale, for example the gravitional atraction beyond some length scale becomes more like 1/r.