Health insurance is a type of insurance that covers some or all medical expenses. It can cover disabilities or long term medical needs, and even just visits to the doctor or emergency situations.
You can purchase insurance through a group or as an individual, and it can also be covered through governement sponsored insurance programs.
A health insurance policy works as a type of contract between you and the insurance company. Usually the contract is a monthly contract, and the rate depends on what type of health insurance coverage you need and which company you sign up with.
Health insurance companies charge based on estimations of the risk for the individual or group, which is why different people and ages may have different insurance rates. Remember, health insurance isn't free, it's a way almost to pre-pay for emergency situations as a society, so that you don't get financially ruined when a disaster arises.