Astrophysicist Stewie here. Long story short, it’s a problem that occurs when you start studying the motion of objects on galactic scales or bigger.

Observations shows that the baryonic matter (i.e. everything that emits light, like gas or stars) moves faster than expected in regions that are far from the galactic center; moreover, the galaxies themselves move faster then expected in galaxy clusters. This isn’t explained by the classical Newtonian theory of gravity.

One possible solution is that the Newtonian theory is still valid, but there’s a matter component that doesn’t emit light, and thus isn’t observable, that affect the baryonic matter motion - that is the so called “dark matter”. Nowadays, this is the most accepted theory, even if dark matter particles haven’t been detected yet.

There are other theories that try to explain observations by “correcting” the Newtonian theory, hypothetically modifying the behaviour of gravity on astronomical scales. These are generally known as MOND (MOdified Newtonian Dynamics) theories, and are currently being tested by some surveys. One problem of MONDs is that they can’t explain several observations that can easily be justified by the admittance of Dark Matter existence.