What is insurance and how does insurance companies work?

The insurance is a contract that is represented by an insurance policy in which a person or company receives financial protection or reimbursement for losses from an insurance company. The company groups the risks of the customers, so that the payments for the insured are cheaper.

Insurance is an arrangement where an entity (insurer) promises to provide compensation to the insured upon the happening of a specified event or loss. This promise can be obtained by paying a small charge upfront (premium). The terms are decided between the insurer and insured via an insurance contract.

how do Car insurance companies make money?

Example - 
the insurer [A] promises to pay the insured [B] a compensation of Rs. 10 lacs (promise) if B is diagnosed with cancer (event) after 6 months from start of policy (terms) and upfront payment of Rs. 2000 (premium).

An insurance company works on building products aimed at providing financial protection from risks. These risks include death of bread earner (life insurance), hospitalization expenses (health insurance), damage to assets (car insurance) etc. The insurance company's role includes -

• a) pricing of the premium
• b) determining the coverage i.e. compensation
• c) inking the insurance contract
• d) collection of premium
• e) administering the claim/promise

The insurance company earns a profit by managing the risk. On a unit economics basis ... Profit = Premium collected + Investment income on premium collected - Selling expenses - Claims paid & provisioned - Operating expenses

Example - 

• Premium collected = Rs. 10 lacs (say, 100 users on avg paid Rs. 10,000 each as premium)
• Investment income = Rs. 80,000 (8% interest p.a. on Rs. 10 lacs)
• Selling expenses = Rs. 1,50,000 (15% commission paid on Rs. 10 lacs)
• Claims paid & provisioned = Rs. 6,50,000 (say, 13% of users made claims averaging Rs. 50,000 each)
• Operating expenses = Rs. 2,00,000 (20% of Rs. 10 lacs)
• Hence, the profit earned by the insurance company is Rs. 1.8 lacs  (Rs. 10 lacs + Rs. 0.8 lacs - Rs. 1.5 lacs - Rs. 6.5 lacs - Rs. 2.0 lacs).
• Please note, while in the above scenario the insurer made a profit - it would have been very different had 23% of the users made a claim instead of only 13%. In this scenario, the insurer would have made a loss of Rs. 4.7 lacs.

Thus, the insurer too has to carry risk on its books and has to manage the delicate balance between risk forecasting and pricing the policy.

Extra : 

Insurance policies are used to protect against the risk of financial loss, both large and small, that may result from damage to the insured person or his property or liability for damage or injury inflicted on a third party.

There are a variety of different types of insurance available, and virtually every person or business can find insurance that is willing to insure them for a price. The most common types of personal insurance are cars, health, homeowners and life. Most people in the United States have at least one of these types of insurance, and the law requires car insurance.