Dark matter is more of an observation than a theory. The gravitational motions of galaxies doesn't really make sense without it (and with dark matter + General Relativity, it fits perfectly, so we have good reason to believe it exists).

There are a few different theories on what dark matter is; there's axions, supersymmetry (from string theory), cold dark matter and more.

Dark Matter is not the same as antimatter, which CERN did produce. There are speculations if there are antimatter galaxies out there and that they are in fact the dark Matter that we search for. But dark matter is in essence matter that should be there, e.g. because a solar system behaves like it is in its gravitational field, but cannot be detected by our instruments. Maybe it is a flaw in our theory, like the time we found out that newtons physic has some flaws, or we can't detect it because it is made of stuff that we can't measure yet.