Are black holes really singularities? Can't black holes just be super dense objects? They could still be black (having the color of black never really required special physics, after all) and have a really strong gravitational field. If we suspect that it actually absorbs light due to its gravity then it is possible that there is gravity strong enough to capture light, not letting any radiate out when matter falls into this object.

I'm just having a hard time accepting that anything can exist with an infinitely large property as it would lead to infinitely large mass leading to infinitely large forces... that would just destroy the universe infinitely fast, wouldn't it? So I think a supermassive object can be a badass just as well without having to be a singularity.
What is a singularity?

A singularity is a point in the universe where matter is infinitely dense. The singularity is at the centre of the black hole, and is often hiding behind an event horizon. So basically, a singularity is a point in space where a lot of matter is squeezed together in a very small space. When you have a singularity matter does not go to infinity. Density is what goes to infinity. Density and matter are different things.

A singularity is often created in a supernova explosion. A supernova is where a star is caused when there is so much matter in the centre of a star (at the end of its life) that the star cannot support its own gravitational force, and it collapses in on itself and explodes.

The second way a supernova can happen is in a binary star system - where if there is a white dwarf, it steals matter from the other star and eventually it accumulates so much matter that it explodes.

A singularity is caused by the big stars, not small ones. Small stars that explode in a supernova create something called neutron stars.

So what is a black hole?

A black hole is a area in space with a gravitational field so strong not even light can escape. Black holes don't have the colour black, they don't have a colour because we can't see any light coming back from them. So no, light is not absorbed. Black holes can also eventually dissipate, due to a mechanism called Hawking Radiation

There are multiple types of black holes including:


Supermassive black holes (often found at the centre of galaxies)
Stellar black holes
Primordial black holes
Rotating (Kerr) black hole


Finally, there are 3 main areas inside a black hole.



This diagram can show us many things, for example, how black holes don't have a gravitational pull which goes across the whole universe.

On a final note, we can work out the area where even light cannot escape by using the Schwarzschild radius. Seen as you said this answer shouldn't include relativity, I won't include any maths either. The Schwarzschild radius, in summary, is where the event horizon is in a black hole.

Summary

Sorry for providing a awkwardly long answer, I was having trouble understanding what you didn't understand, and I thought that if I explained a singularity - then I'd surely help you, sorry if I've just said things you already know. I've provided some Wikipedia links if you want to have a look at some of the terms I left in italics. You might also want to look at black hole thermodynamics


Schwarzschild radius
Ergosphere
Hawking radiation
White dwarf
Black hole thermodynamics