A black hole is an incredibly dense remnant of a star that has collapsed under its own gravity after running out of hydrogen fuel. The resulting body is too massive to counteract its own gravitational forces, and therefore collapses into itself. Black holes have extremely strong gravitational fields, similar to cosmic string fragments. The gravitational force of a black hole is so powerful that even light cannot escape.
The late-20th century NASA probe Voyager 6 disappeared into a black hole, emerging on the other side of the galaxy, where it came into the posession of a race of sentient machines. The machine race constructed a massive vessel around the probe to facilitate its mission of acquiring all knowledge, and it began its journey back to Earth. As of 2152, Vulcans had charted over 2,000 black holes.
In 2152, the Enterprise NX-01 encountered a black hole that was part of a trinary system, something unheard of by either Starfleet or Vulcan scientists. Attempting to study the black hole, the Enterprise crew became affected by an exotic form of radiation which caused nearly all members of the crew to exhibit irrational and obsessive behavior. Subcommander T'Pol, whose Vulcan physiology was immune to the radiation, performed an analysis which indicated that prolonged exposure to the radiation would be fatal to the crew, forcing her and Captain Archer to navigate Enterprise through a hazardous debris field in order to escape the influence of the radiation in time.
In 2366 the USS Enterprise-D engaged in an operation to stabilize the moon of Bre'el IV, which was in danger of crashing into the planet. The crew was informed by Q that the the deterioration of the moon's orbit was most likely caused by a black hole passing through the solar system's plane at near-right angles.
Black holes are surrounded by event horizons, the boundary at which light can no longer escape. In 2371 the USS Voyager became trapped within a black hole's event horizon and experienced unusual temporal and spatial distortions. Voyager was able to escaped by using a dekyon beam to open a hole in the event horizon.
Black holes are naturally occurring but similar to artificial singularities, such as those used by 24th century Romulan starships or the Hirogen communications network relay station encountered by Voyager in 2374.
The Quantum singularity lifeforms need a gravity well to incubate their
young and mistook the artificial engine core of a Romulan warbird for
a black hole.
A black hole can be artificially created by the ignition of a small amount of red matter. Such a phenomenon caught the vessels Narada and Jellyfish following the use of red matter to create a black hole to absorb the supernova of 2387.
See the original version at Memory Alpha