An annuity is a product. In simple terms, you hand over a lump sum of cash and receive an agreed annual income until you die. The underlying investment required to reach that income level is not your concern, it's the provider's worry. So there is a huge mount of security to the retiree in having an annuity.
It is worth pointing out that with simple
annuities where one gives a lump sum of money to (typically) an insurance
company, the annuity payments cease upon the
death of the annuitant. If any part of the lump sum is still left, that
money belongs to the company, not to the heirs of the deceased. Fancier versions
of annuities cover the spouse of the annuitant as well (joint and survivor
annuity) or guarantee a certain number of payments (e.g. 10-year certain)
regardless of when the annuitant dies (payments for the remaining
certain term go to the residual beneficiary) etc.
How much of an annuity payment the company offers for a fixed lump sum
of £X depends on what type of annuity is chosen; usually simple annuities
give the maximum bang for the buck. Also, different companies may offer
slightly different rates.
So, why should one choose to buy an annuity instead of keeping the
lump sum in a bank or in fixed deposits (CDs in US parlance), or
invested in the stock market or the bond market, etc., and making
periodic withdrawals from these assets at a "safe rate of withdrawal"?
Safe rates of withdrawal are often touted as 4% per annum in the US,
though there are newer studies
saying that a smaller rate should be used. Well, safe rates of
withdrawal are designed to ensure that the retiree does not use up
all the money and is left destitute just when medical bills and other
costs are likely to be peaking. Indeed, if all the money were kept in
a sock at home (no growth at all), a 4% per annum withdrawal rate will
last the retiree for 25 years. With some growth of the lump
sum in an investment, somewhat larger withdrawals might be taken in
good years, but that 4% is needed even when the investments have
declined in value because of economic conditions beyond one's
control. So, there are good things and bad things that can
happen if one chooses to not buy an annuity.
On the other hand, with an annuity, the payments
will continue till death and so the retiree feels safer, as Chris
mentioned. There is also the serenity in not having to worry how
the investments are doing; that's the company's business.
A down side, of course, is that the payments are fixed and if inflation
is raging, the retiree still gets the same amount. If extra cash
is needed one year for unavoidable expenses, the annuity will not
provide it, whereas the lump sum (whether kept in a sock or invested) can
be drawn on for the extra expense. Another down side is that any money
remaining is gone, with nothing left for the heirs.
On the plus side, the annuity payments are usually larger than
those that the retiree will get via the safe rate of withdrawal
method from the lump sum. This is because the insurance company
is applying the laws of large numbers: many annuitants will
not survive past their life expectancy, and their leftover monies
are pure profit to the insurance company, often more than
enough (when invested properly by the company) to pay those old
codgers who continue to live past their life expectancy.
Personally, I wouldn't want to buy an annuity with all my
money, but getting an annuity with part of the money is
worthwhile.
Important: The annuity discussed in this answer is what is
sometimes called a single-premium or an immediate annuity.
It is purchased
at the time of retirement with a single (large) lump sum
payment. This is not the kind of annuity that is described in
JAGAnalyst's answer which requires payment of (much smaller)
premiums over many years. Search this forum for variable annuity
to learn about these types of annuities.