The standard scientific one-liner to explain Black Holes is generally along the lines of "a black hole is an object which has gravity so strong that not even light can escape it." This is technically accurate, however it implies things that are simply not true.
First and foremost is the idea that black holes have stronger gravity than other objects in the universe, that they act as stellar vacuum cleaners sucking up everything around them. To give an example, imagine this: What would happen if the sun was suddenly and instantly transformed into a black hole of equal mass?
The statement that "black holes are objects that have gravity so strong that not even light can escape them," implies that the planets would get sucked in because the black hole's gravity would be stronger than that of the sun and pull everything into it.
However if the sun was replaced with a black hole of equal mass, the planets would not be sucked into it. In fact, the orbits of the planets would not be affected at all, and the solar system would continue as it always has, albeit much darker and colder without the sun providing energy.
So, a black hole does not possess any more gravitational strength than any other object of equal mass. Yet, it also possesses gravity strong enough to prevent light from escaping. How is this possible? To understand this apparent contradiction, it is necessary to talk about gravity in general.
The attractive force of gravity between two objects is expressed by this equation:

Now, the center of mass for an object is fairly simple. Lets take the sun as our example.

Imagine that every single part (Whether you want to think of regions like top/bottom, or individual atoms) of the sun has its own rope that it is using to pull on the Earth.
Now, think of these 'gravity ropes' as vectors, as in the image below:

The advantage of thinking about gravity in terms of these vectors, at least for the time being, is that it simplifies very well. As you can see, each vector has a horizontal component and a vertical component.
Now, since the sun is (mostly) spherical, there is an equal amount of matter at the top, bottom, left, right, and everything in between. What this means is that the vertical components of these vectors tends to cancel out, like so: This leaves only the horizontal components, which pull the matter directly towards the sun. The center of the sun to be specific, because no matter what direction you move towards the sun, gravity will always pull you directly towards it. The fact that some matter is further away from you is countered by the fact that the same amount of matter is closer to you, giving a center of mass at the center of the object.

So why is this important? As it turns out, in objects like stars or planets, the gravity is strongest at the surface of those object. As you read this, you are feeling the strongest pull that the planet Earth can put on you. If you move away from Earth, you are increasing the distance between you and the Earth's center of mass and the strength of gravity becomes less. But if you move down into the Earth, you are reducing the distance between yourself and the center of mass and so gravity should get stronger right? Remember, that all matter attracts all matter individually. Right now, on the surface of the Earth, all of the matter is pulling you down towards the center of the planet. However, once you are underground, two things change. First, you have less matter pulling you down and second, you have matter above you which will be pulling you up, as this picture shows:

And now we can correct one of the biggest misconceptions about black holes. They possess no more gravity than another object of the same mass. However, black holes are singularities, meaning that you are never 'inside' them. All of the matter is always pulling you down, no matter how close to it you are. The gravity always gets stronger, and this allows something with the same amount of mass to have more powerful gravity effects.
So, describing a black hole as a vacuum cleaner is not accurate. It does not 'suck things in', any more than what other objects do. Rather, black holes are the stereotypical cranky old men that won't let you get basketballs/baseballs out of their yard.
So long as you keep your distance, black holes are no different than any other object. But once you get too close, you never get a chance to learn from that mistake.
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