Why does time get slow near a black hole? Why exactly does time get slow around a black hole? And does it provide a way to go into the future?
The simplified answer is: Due to gravitational time dilation.

That's a consequence of general relativity. One fundamental idea of general relativity is the equivalence of inertial and gravitational mass, meaning forces induced by acceleration aren't distinguishable from gravity.
Persuing this principle together with the constant speed of light lead to Einstein's field equations. One of the solutions of these equations is the Schwarzschild solution for non-rotating, electrically neutral black holes.
This solution can be used to derive gravitational time dilation, as part of spacetime warp near mass/energy.
(Introductory video to general relativity)

A black hole provides a way to go faster into the future of a region of higher gravitational potential away from the black hole.
But the body near the black hole needs to withstand the high gravity. Circular orbits around a black hole are only possible down to 3/2 times, stable only down to 3 times, the Schwarzschild radius.