I'm gonna talk about charge, essentially the same thing happens with spin, but it gets a bit more complicated. The TLDR is this, charges with the same sign rep

I'm gonna talk about charge, essentially the same thing happens with spin, but it gets a bit more complicated. The TLDR is this, charges with the same sign repel each other, if you're trying to make a black hole have more and more charge you have to do more and more work to push the charges you're adding into it (imagine forcing the repulsive poles of two magnets together as one of the magnets gets stronger and stronger). At an extremal black hole it is no longer possible to push hard enough to force the charge to get into the black hole. A more interesting thing is to look at the event horizon. First take a look a the quadratic function x^2 - a, for some positive real value a. Let's say we start at a=1, then the equation x^2 - 1 = 0 has two solutions, x=1 and x=-1, the function looks like a "u" shape passing through these points. Now let's make a smaller and smaller, this shifts the u shape up, and the two solutions of the equation at plus or minus the square root of a get closer together. When we hit a = 0 there is only 1 solution, and when a is strictly positive there are no real solutions anymore. Thus is roughly what happens to the event horizons of a charged black hole as you increase the charge. A charged black hole generically has two event horizons, an inner one and an outer one. As you increase the charge (while keeping the mass constant) the event horizons get closer and closer together. At the charge for an extremal black hole the two event horizons are in exactly the same place (the same as our quadratic when a=0), above this extremal charge there is no event horizon anymore. We don't really have a good idea of what a black hole with no event horizon looks like, the event horizon of a "normal" black hole shields us from whatever insane physics is going on inside (general relativity predicts a singularity with infinite density in the middle). Most physicists believe that it is impossible for a black hole to exist with no event horizon.