Purity refers to the amount (by weight) of pure gold or silver an object has. The most common way of describing purity is by Carats (Karat in the US). Carats are just the purity expressed in units of 24, such that 100% equals 24 carat and 50% equals 12 carat.
Carats are used primarily in the jewellery industry. For bullion, the industry uses either percentages or fineness (fine being another word for pure). The table below shows the most common purities.
||750 on jewellery
||585 on jewellery
In verbal discussions, 99.99% is often referred to as "four nines" and 99.9% as "three nines". Products equal or greater than 99.5% pure are generically referred to as "nine nine five".
In the wholesale investment precious metal markets, physical gold is traded in bars of approximately 400oz with a purity of 99.5% or more. For silver, the market trades in 1000oz bars of 99.9% purity. The reason wholesale gold is traded at 99.5% is because it is much cheaper to refine to this purity than 99.99%, which requires additional processes.
In retail markets, customers usually prefer coins and small bars with a purity of 99.99%, notwithstanding the additional cost. However, the 22 carat American Eagle and South African Krugerrand gold coins are very popular.
Silver is usually only sold as 99.9%, although "four nines" silver coins are available. Investment platinum is mostly sold at a purity of 99.95%.
Purities greater than 99.99% are only really useful in certain industrial/scientific equipment and processes where the small impurities control the electrical and mechanical properties of the metals.
There are international standards on determining the purity of a product. For example, Australian Standard 3515.4-2007 says that for something to be called 99.99% the minimum purity has to be 99.9875%.