Yes, a basic intuitive explanation can be had without a lot of fancy math.
Imagine a pile of stuff in space. Every bit of stuff has gravity, which pulls every other bit of stuff towards it. If you pile enough stuff, it will all be squished together by gravity and make a ball. The earth is a good example of this.
The earth is a big enough pile of stuff so that a little jostling of the stuff won't make any fly off. For example, when you throw a rock upwards, hit a baseball pop-fly, or a volcano spews rocks into the air, they all fall back down. In fact, there is something called escape velocity, which is how fast you'd have to fire something upwards for it to be able to leave the pile of stuff and not eventually fall back down. The bigger the pile of stuff and the closer you are to it, the faster the escape velocity is. On the surface of the earth, the escape velocity is around 11 km/s. That's way faster than a speeding bullet.
Now imagine piling on more and more stuff. Imagine how squished things in the center of the pile must be getting. The pressure in the center of the earth is very high in human terms, but not high enough to do anything interesting with the stuff (mostly iron at the center of the earth) there. However, if your stuff was hydrogen instead of iron, eventually the very high pressure and high heat resulting for squishing it so much will cause the hydrogen atoms to fuse in to helium. That's called a star.
Our star is a much bigger pile of stuff than the earth, and the escape velocity at its surface is a lot higher than the earth's piddly 11 km/s.
Now keep piling stuff. The center gets more and more squished and therefore smaller, and the escape velocity gets higher and higher. What if you could pile so much stuff that the pile gets so small and squished but also so massive that the escape velocity reaches the speed of light? Since you can't make stuff go faster than the speed of light, there is no way to make it go fast enough to ever leave. That's a black hole. We call it "black" since not even light can escape, so it doesn't radiate light.
So from this you should be able to see that a black hole is a combination of a very large pile of stuff in a very small space.
I glossed over a few details in making a black hole, since those weren't immediately pertinent to your question. In reality, if you made a bigger and bigger pile, you'd get more and faster nuclear reactions as more and more stuff got squished and heated. That causes outward pressue which would keep the pile from compressing more, preventing it from getting small enough to be a black hole. You just end up with a super-bright star.
However, eventually what started as hydrogen is converted to heavier and heavier elements and the nuclear reactions are no longer sustainable. Before that the star goes thru some convulsions which also make it very big, meaning it's stuff is spread out over a large radius. Our sun will eventually get large enough to include the orbit of earth, for example.
When the nuclear reactions eventually run of of material that can be profitably fused, the outward pressure from the enourmous power of those reactions ceases. Imagine something the mass of our sun with its associated large gravity spread out in a sphere the size of earth's orbit. All that stuff is being pulled inward by gravity. It was held out there by the outward pressure caused by the nuclear reactions. When those cease, there is nothing left holding the stuff out there. Now it's going to fall back down towards the center. Considering there is a solar mass of stuff to fall and it has 100 million miles to fall, it's going to make quite a mess when it all comes crashing in on itself. That's called a nova.
If the star was heavy enough, then the pressure from the momentum of all that mass falling and crashing together causes such high pressures that enough of the stuff at the center is squished enough to form a black hole. If I remember right, it takes about 4 solar masses for that to happen.
The really big ones are called supernovas. A black hole is formed in the core, but the stuff just outside that still got so hot and so squished so that just about every imaginable nuclar reation took place. This is where all the bizarre elements come from. They are produced in the last momements of a large star collapsing in on itself. These nuclear reations gone amock now release so much energy that the star isn't just pushed out again to become bigger, but is blown to smitherenes. You end up with a black hole in the middle and everything else making a ever-expanding shell of stuff flying outwards at a good fraction the speed of light.