An annuity, in financial theory, is a series of equal fixed payments made at regular intervals that terminates at some point. A similar stream of payments that does not terminate is called a perpetuity.
An annuity is also a financial produce, usually purchased from a life insurance company, that pays a regular income until the death of the purchaser in return for a lump sum. The insurance company needs to use the lump sum and the income they get from investing it to meet the annuity payments. As the length of any person's life is uncertain the insurance company bears a risk.
A life assurance policy can be thought of as the opposite of an annuity. With a life assurance policy, the insurance company makes a loss when each insured person dies within the term of the policy as it has to make a payment. With an annuity, the insurance company makes a gain when each insured person dies.
The opposing natures of annuities and life insurance means that the annuities an insurance company sells hedge certain risks to its life policy payouts and vice-versa. For example, if the death rate rises then the insurance company will have to pay out more on life policies but less on annuities.