What are detached black holes? I understand what black holes are, and how they form, but I was recently introduced to the topic of detached black holes. What are they and how are they different from standard black holes?
A detached black hole is simply a black hole that is not part of a close binary pair.
There are two ways that we can detect stellar mass black holes. Firstly when they are close to a star, and matter is flowing from the star into a disc around the black hole.  Matter in the disc will orbit at substantial fraction of the speed of light, and friction will cause it to heat up to extreme temperatures, hot enough to emit X-rays.  If we can detect these X-rays and we can work out the mass of the object, we can deduce the existance of a black hole.
The second way is through gravitational wave astronomy, detecting the gravitational waves emitted when two black holes merge.
Detached black holes, that don't have a partner, are much harder to detect.  As there would be no disc of hot matter they would not emit x-rays.  In fact they would not emit anything. A detached black hole could be part of a binary system, but far enough from the star that no matter transfers from the star to the black-hole.  Such a black hole could be found by observing the radial velocity of the star. The gravity of the black hole will cause the star to orbit around it, the forwards and back motion of the star can be detected and the mass of the object can be deduced.  A large but invisible mass is a likely black hole.  See A detached stellar-mass black hole candidate in the globular cluster NGC 3201