As a general idea, it's pretty simple. They get money from premiums that you and I pay. Then they invest that money and generate investment revenue from our premiums. In fact, most insurance companies pay all claims which are made each year out of the premiums they take in from you and I. The investment returns create profit for the insurance company. See the following links for background on how insurance companies make money.
Why is how insurance companies make money important? 
Well, we don't need to feel like we are doing something wrong when we make a claim.  They have plenty of money to pay claims. And if some natural disaster occurs, they have easy ways to increase their rates without much supervision or legal protections to consumers. (See the earlier article in the installment of articles on insurance rates). Secondly, if we ever get to sit on a jury in a case where the insurance company is responsible for paying the claim (you probably won't know because whether there is insurance coverage is available is not admissible evidence in many states) we should NEVER be concerned with how our decision as jurors might affect insurance rates. Most civil claims are covered by insurance.  In Georgia, most lawyers and judges will tell you specifically not to base your decision on speculation on such issues that are not part or the evidence in a case. Almost as important, a jury verdict will not cause problems for the financial health of an insurance company.