Einstein's Theory of relativity is definitely one of those few theories in the history of physics,   that changed the way we see things. It revolutionized the cosmology in such a way that many physicists who are struggling in their respective lines of research produced some shockingly interesting results.

Black holes is one such shocking yet interesting result and in fact is a revolution.

So, what is a black hole?

Well!, there are a lot of definitions, and in the simple possible way: A Black hole is a region in space-time with such an immense gravitational pull towards its center that even light cannot escape out of it.

How is Einstein's 'Theory of relativity' responsible for its formation?

Black hole is a subject almost entirely based on theoretical evidences rather than physical evidences(strong). All these theoretical proofs are in fact implied from the Theory of relativity.
To get some idea about its formation and stuff, we must know the life cycle of a star as a prerequisite.

A star takes birth when large amount of nearby gaseous particles(mostly hydrogen) attract towards each other and get squeezed.
In this process of contraction, particles collide with each other to produce large quantities of heat energy. This heat is what responsible for the star to shine brightly!. The heat produced would be  so immense that, particles when they come closer will no longer collide but coalesce, and forms higher elements like helium, Lithium, Berilium...along with some amount of heat. Heat that got released in this process, creates high pressure between the particles and tries to drive them away, opposing the contraction process. The more the star tends to contract, the more will be the opposing pressure.
At some stage there will be a perfect balance between the contraction(force) and expansion(force)  making the star remain stable. And the star remains stable for quiet a long period of time(million millions of years) until one of its forces gets weaker. Obviously, it can't be the gravitational force(contraction) that gets weaker.
The pressure inside the star eventually gets weaker, and the denser particles that gets cooled  drift towards the center of the star, re surging the contraction. This process continues until it reaches a stage where, the contraction force gets balanced through the repulsions between subatomic particles(electrons, protons, and neutrons). The star remains stable again.

The star that gets balanced through the repulsions between 'electrons'  is called as a
'White dwarf' with a radius of about few thousand miles and with a density of about hundreds of tons per cubic inch. The one that is supported through the repulsions between protons and neutrons is popularly called as a 'Neutron star' with a radius of about ten miles(only)  and density, hundreds of millions of tons per cubic inch.

This would be the final stage of every known and unknown star that exist in our known and unknown universe, if the subatomic particles able to move with out a limit. But, according to Einstein's Theory of relativity, nothing can travel faster than light.

Here comes the interesting question: What if the star is so heavy that it requires the electron(or proton or neutron) to move faster than light--to balance the immense contraction(force)?

These kinds of movements or repulsions among the subatomic particles are impossible as per the Theory of relativity and hence the star ends up in a gravitational collapse, and forms an infinitely dense region, popularly known as a 'Singularity'.
The star that gets vanished in to a 'singularity' still exerts the same, finite light trapping gravitational pull(can be more but not less) up to certain distance in space creating a 'Black hole' around it. The boundary of this 'Black hole', the 'Event horizon' is formed by the paths of light just managed to move around but can't escape.

Thus the whole Black hole formation was almost based on Einstein's 'Theory of relativity'.

What if the electrons under those special conditions(gravitational collapse) could move with out a speed limit--faster than light ?

There will be no 'Singularity', no 'Black hole', but will be a 'Black star' or 'Dark star' that still can trap light.