MOND is the short name for Modified
Newtonian Dynamics. It is one of the possible answers along with
dark matter for an explanation of why we stars and galaxies are moving as they do (something more is needed as the laws and theories existing prior do not properly explain what is seen). It is a modification of
Newtonian force law that was hypothesized in 1983 as an alternative to
dark matter.
The modification can be interpreted as either a modification to gravity or a modification to inertia. This modification occurs at very small accelerations. Above a critical acceleration (a0), everything is normal. Below a0, the effective acceleration approaches a = (gN a0)1/2, where gN is the normal Newtonian acceleration. a0 = 1.2 * 10-10m/s-2, or about one angstrom per second per second. This is one part in 1011 of the gravity that is felt on Earth.
MOND was designed to fit the rotation curves of spiral galaxies that are currently explained with dark matter. It is often claimed that MOND is ad hoc and thus bad. However, this is also true of dark matter which was hypothesized to explain the rotational curves of spiral galaxies. One of the advantages of MOND over dark matter is that it does not cause any extra problems with a Newtonian disk and a dark matter halo.
MOND does not contradict General Relativity as they apply to different ends of the extremes of velocity. Relativity is what happens as v -> c, while MOND is what happens as a -> 0.
Empirically, MOND works. There is no empirical evidence that clearly contradicts it. Its predictions come true where those of dark matter based theories fail.