A black hole is a region of space-time wherein an extremely strong gravitational field prevents anything, including light, from escaping. It is a dense remnant of a star that has collapsed into a singularity under its own gravity upon running out of fuel.
The current consensus is that super-massive black holes are at the center of most, if not all, galaxies.
The intense gravity of a black hole also causes severe time dilation nearby, as well as redshifting electromagnetic radiation sent out of the gravity well. A starship can use its warp drive to partially counteract the time dilation effects. (Bait and Switch: "A Changed World")