Gravitational collapse happens when the density of the matter is so high that the force of gravity overcomes the other fundamental forces that keep matter together.
Normally the strong nuclear force keeps atoms from interlacing with each other. Similarly the weak force keeps the subatomic particles apart. These two forces are much stronger than gravity at short distances. Until the density of matter becomes big enough for gravity to overcome them. The limit where the matter becomes dense enough to start collapsing into itself is the same as the point of no return e.g. the Schwarzhchilds radius.
Imagine you had a bag of ping pong balls. The bag can only fit a certain amount of those balls. But if you apply enough force the walls of the balls will give in and you can fit a lot more, although now useless, balls in to the bag. That's essentially the same thing that happens to the atoms and even the subatomic particles when they become under enough force. When there isn't anything holding the particles apart anymore against the gravitational forces these particles will be pushed infinitely towards each other in an endless free fall at that single infinitely dense point of space-time.