My understanding -please correct me if I am wrong- is that the definition of a black hole is strictly mathematical. A black hole is just the mathematical solution to formulas derived from General Relativity.That is the reason why their existence was factually determined a long time after their "discovery" as series of numbers in a piece of paper...(Exploiting the microlensing effect is currently one of the ways to detect the 'footprints' of a black hole)
The simplest black holes are spherically symmetric.(Non-rotating ones). For any spherically symmetric object one may define an imaginary sphere around it of radius rs = 2GM/c^2, where G is the universal gravitational constant, M the mass of the object and c the speed of light in vacuum. (Very peculiar, even though this formula is deriving from General Relativity, aren't you recognizing a pattern fitting right into Newtonian laws....?).
This formula tells us that the radius of the black hole is directly proportional to the mass of a black hole, i.e. the more massive the black hole the larger the radius.
The rs factor is called the Schwarzchild radius.
If the surface of ANY object is at a radius less than it's rs, then this imaginary sphere is called the event horizon and the object is called a black hole. Note that if the radius of the surface of ANY object is larger than rs then there is no event horizon and the object is not a black hole but something else instead...
Now as far as the observable universe is concerned:
At first, let us see what does "observing" or "seeing", really entails..?
Initially, there has to be light present (photons that is...)
Again -from what I've read- when light (photons) enter the eye, they reach the retina, which is the light-sensing structure of the eye, and by triggering it (coming in contact with the eye's photosensitive part) we are enabled to perceive our cosmos through the miracle of vision, right...?
Ok, now taking in consideration the fact that light travels at 300,000 kilometers per second for all observers (according to our predominant current theories) we can conclude that if the Universe were only one second old, an observer would not be able to see things which are more than 300,000 kilometers away because there would not have been sufficient time for this light to propagate that far...
So at each point in the history of our Universe there a distinct radius (a horizon) which is self-determined -pretty much- by the distance that light could have traveled since the birth of our Universe....As our Universe ages, the horizon expands outwards because there is more time for light to travel & on top of that our Universe itself is expanding with a slightly accelerating rate...
Logic states that if we cannot 'see' beyond the 'horizon', then neither can we be affected by any physical effect from beyond that horizon. Regions of space in the Universe which are separated in distance by more than the horizon, simply do not 'know' about each other, and cannot influence each other's physical conditions....
Therefore we choose to exclude those hypothetical 'parts' of our Universe (...?...or someone else's Universe) from our calculations and models and just say that we just don't care ! (very-very simplified...)
As a new member of your community, I hope I have slightly contributed to this thread with my post. Happy to be here.