You pay premiums, I pay premiums, laodaron pays premiums for just liability (or any other coverage actually) to say... State Farm.
And lets say I am the one that crashed in to someone's house and causes property damage.
All of YOUR premiums are in the pool of money that pays the claim.
Now, lets say all three of us have health insurance with the same carrier, and only Laodaron gets sick and has big medical claims.
All of OUR premiums go to paying HIS medical claims.
That's the simplified version.
Now imagine that instead of those premiums, you are paying taxes...