How do insurance companies earn and gain profits if they are paying people for their losses?

I just don't understand how they work, because I have never really taken any interest in it. But my dad recently hit a cop-car, and both the cars were badly damaged, and the insurance paid for the damage. That was certainly not a cheap amount, so how do they earn if they are spending on people? Do they take... show more I just don't understand how they work, because I have never really taken any interest in it. But my dad recently hit a cop-car, and both the cars were badly damaged, and the insurance paid for the damage.
That was certainly not a cheap amount, so how do they earn if they are spending on people?
Do they take money from people when they sign up for an insurance?
I'm sure my dad did not pay THAT much for his insurance, so how do the insurance companies manage and run their buisness?
Or are they payed by the government?
Also, what are policies and claims?

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Update: LB Centaur, could you please clarify?
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