My question for you today is about how big does the remaining core of a supernova have to be to collapse and become a black hole? If you want, could you please explain to me about how nothing, not even light, can escape a black hole.(I'm just curious.)
The limiting mass is determined by that for neutron stars, which cannot be more than 2 to 3 times the mass of the Sun (the exact number is not known, because it depends upon theories of ultra-high-density physics that are of uncertain accuracy). If the core of the supernova exceeds the neutron star mass limit, then it will collapse to a singularity, which is the central point of a black hole.
It is also possible, though not as likely, to have black holes of lower mass. In a supernova, an implosion of the central core leads to an explosion of the outer regions. Depending upon how the energy of the explosion drives material outward and/or inward, the central core might be compressed to a singularity even if it has a mass well below the limiting mass of a neutron star.
So at the moment all we can say is that if the core left behind by a supernova is well over 3 solar masses, it will definitely become a black hole; and if it is less massive than that, it may become a neutron star, or it may become a black hole.
What makes a black hole is the compression of the remaining material into a point mass called a singularity. If matter is compressed into a region smaller than its "Schwarschild radius", the inward force of gravity becomes greater than any opposing force, and the matter is crushed to zero size and infinite density (though no more mass than before its collapse). In a small region close to the singularity, gravity is so strong that the space-time near the singularity is falling inward at a speed exceeding the speed of light. So even if something was moving outward relative to its nearby space-time at the speed of light, since that space-time is falling inward at more than the speed of light, the objects contained within it have a net inward motion. (If you would like a discussion of how space-time falls I can cover that, but I have to accompany someone to their doctor in a few minutes, and don't have enough time to do that right now).
As you move away from the singularity its gravity decreases, and the rate of fall of space-time also decreases. Eventually, at the Schwarschild radius, the inward fall of space-time is equal to the speed of light. Anything going slower than that inevitably falls into the singularity, but light headed directly outward can 'hang up' at that distance from the singularity (at least in principle; in practice, it would probably also eventually fall inwards, for reasons beyond the scope of this brief reply).
Because of the above, anything closer to the singularity than its Schwarschild radius can never escape, no matter what it is, or how fast it is moving relative to the inward fall of space-time near it. That is why the region inside that distance is called a "black hole" -- something like a hole, in that nothing can get out of it, and black, in that no light can escape it. The "surface" of the region is called the event horizon, because nothing that ever happens inside that surface (that is, no "event") can ever be observed from the outside.
As you move still further away from the singularity the inward rate of fall of space-time becomes less than the speed of light, and objects (and photons of light) that are headed directly away from the singularity at the speed of light or nearly that speed can escape into interstellar space.
(As noted above I need to leave very soon, so I'm afraid that's all I have time for right now; but I'll be happy to elaborate on any part of this after I return, sometime this afternoon (or evening, depending upon your time zone).
(Several hours later: corrected a mis-spelling of Schwarschild radius; otherwise, things have been left as-is, pending receipt of a followup to the question.)