Insuring your own life isn't done for yourself but for those you care about. It helps reduce the financial cost of unexpected death by paying money to the insured's benefactors. Otherwise they may find themselves unable to pay bills or the mortgage.
In order to get life insurance you have to sign a contract with a life insurance provider. This is done between the policy owner and the insurer. Note that the policy owner doesn't have to be the one insured but they are the one paying the premiums. The policy gets paid upon either death of the insured or on similar terms. It is possible to have it pay out if the insured contracts a serious or a critical illness. Normally the life policy has two aspects; there is the death benefit, which is a lump sum payout, and the savings component, which is a funds account.
There are two basic types: term and whole life insurance.
Term life insurance pays only if the death occurs within a specific term, normally up to thirty years. They are fairly simple policies and normally don't have any other benefit provisions. The basic term policy is 'level term' which means that the payout is constant over the period. There is also 'decreasing term' where the payout drops over time.
Whole life insurance, or permanent life insurance, pays whenever you die, no matter how long that is. It can be broken down into three types. There is 'traditional' whole life, where the payout and the premium stay level but are still determined according to the risk of death. Traditional whole life is the most common. It pays out a death benefit, which is fixed, and also a savings account, which can grow over time. Universal whole life or adjustable whole life is designed to have a lot more flexibility. Your premium isn't fixed but is able to be altered depending on your financial situation. Lastly there is variable whole life. Here you have more control over the saving portion. You have the choice of a variety of investments but you also share the risks. If the investments don't perform well you could end up worse off.
While life insurance is generally used to gain a peace of mind it can also be used fraudulently.
Some try to use life insurance as a kind of investment. This is referred to as STOLI or Stranger Originated Life Insurance. This is where a stranger approaches someone, generally an elderly person and offers to take out life insurance on them. The insurer is listed as the benefactor, so upon the insured's death they get the payout. While a life insurance policy requires constant payment the investor is effectively wagering that the person will die sooner rather than later so that the payout will be less than the fees.
There is also the more dramatic situation where a life insurance policy is taken out then the insured person killed. Keep in mind that insurance companies generally require the policy owner to have what is called 'insurable interest'. That means that they have to have a benefit that will be lost upon death. This generally covers family as well as business partners.