Simply put an 'annuity' is a series of payments made at regular intervals. Thus annuities encompass a wide variety of financial tools used to generate income. Examples of annuities are securities, bonds and equity all of which are based around the fundamental time value of money. For example suppose you were owed 20 dollars would you prefer 20 dollars repayment now or 20 dollars repayment in a month? Any rational decision maker would prefer 20 dollars now and there are a number of good reasons why. Firstly money in your pocket today is certain whereas the money given in the future isn't. Hence there is risk involved in you receiving a payment at a later date because of unforseen events which could stop you receiving your money. Secondly inflation will devalue the dollar over time meaning the 20 dollars in a month is valued less than the 20 dollars now (in consumer terms). This may be rather insignificant over such a short period but it's still worth taking into account as it is a great risk to the investor. Exposure to inflation is one of the biggest dangers when taking on most types of annuity as it is destroys the purpose of receiving fixed payment. Lastly there is the "opportunity cost" of leaving your money with somebody else (the marginal cost of making the decision to tie up ones fiscal resources) that the lender needs to be compensated. This has everything to do with the nationally set interest rate. The nationally set interest rate is essentially a 'risk free' interest rate (also known as the yield) offered by the government. This means that if you were to make an investment with the government at a safe but nominal interest rate why would you instead choose to take on the risk of another investment if you are not compensated for that risk? In our example a rational decision maker would accept 20 dollars now and invest it at the current interest rate hence growing their investment instead of both risking their money and losing the interest you could earn 'risk free'. The time value of money is vitally important to understanding annuities because an annuity is a future payment of funds for a current investment.
A security is a common form of annuity and it is usually issued by an ADI (commercial bank) to an investment bank that will then assemble multiple securities and offer it to investors (or instead to the Reserve bank to provide liquidity to the ADIs). It is a contractual loan agreement made by a creditor (loan issuer e.g. a bank) which can be sold. Upon purchasing a security you are buying this agreement between a borrower (e.g. a person buying a house) and a creditor (e.g. a bank). In investing in security you are giving over a lump sum (the purchase price) for a series of equal payments (aka an annuity). Securities are invaluable to the financial system as they allow liquidity (ease of access to funds/ability to sell) for commercial banks as well as other creditors and investors. Securities also happen to be one of the root causes for the 2008 financial crisis. However the most significant cause being a result of incentives problems and informational asymmetries. For more information on the 2008 financial meltdown I recommend watching the series "The ascent of money" and "Inside Job".
Equity is another form of annuity known as a perpetual annuity; equity, also known as stock, is an investment in ownership a company. When you purchase equity many big companies (such as Telstra) issue what's known as dividends. Dividends are payments from the company to the stockholders (equity holders/owners) of that company. Equity is known as a perpetual annuity because there is no foreseen expiry date to these payments. This is where equity differs as an annuity to bonds or securities because securities and bonds have an expiry date. The annuities of a security are no longer paid once the loan is paid off (which is similar to a bond). Therefore securities have an upper limit to how much capital (return on investment) they bring to the investor. Whereas equity has no upper limit a person can keep gaining on their investment. The drawbacks of equity are there is no requirement of a company to pay dividends (a company can choose whether or not to pay dividends at all) and on top of that an investor can lose their entire investment if the stock were to plummet in value. This is the advantage of Securities and bonds they are legally enforced if a person is to default on payments their own assets are liable. This protects the investment of the investor (many securities and particularly bonds are guaranteed by government lessening the risk but not eradicating it.) making a security a 'safer' annuity than equity.