The technical definition a Satoshi is that it is one hundred millionth of a Bitcoin, or it is the smallest unit of the Bitcoin currency recorded on the block chain. The name Satoshi comes from the creator of bitcoin Satoshi Nakamoto.
Satoshi is actually used on the block chain to describe the currency before it is put out on the network. In addition, many use the Satoshi denomination as a way to provide easier readability when describing a fractional amount of Bitcoin.
There are other values based on the Satoshi like, millasatoshi, which is one hundred billionth of a Bitcoin. This is used by some payments and exchange processors in order to identify small amounts of transactions. Some other terms that correlate more closely to Bitcoin are also use, like, millibitcoin, and microbitcoin. Each of these have different denominations, but like the Satoshi, are used to name fractional values of Bitcoin.
Despite what some people may say, there is no unified, agreed upon symbol of the Satoshi. Some folks have used the abbreviation sat and others have used s. Other Asian symbols or alphabet characters may seem to mean or spell Satoshi, but there is no clearly defined symbol for Satoshi.