A satoshi is the smallest unit of Bitcoin, equal to one hundred-millionth of a single bitcoin. It produces a way to price, send, and account for very small amounts of Bitcoin without dealing in fractions of a whole coin.
The unit is built into Bitcoin's design: one bitcoin divides into 100,000,000 satoshis, so amounts can be expressed precisely even when a single bitcoin is worth a large sum. Small payments, fees, and micro-transactions are often quoted in satoshis rather than as long decimal fractions of a bitcoin.
The relationship mirrors cents to a dollar, with one difference of scale: a dollar splits into 100 cents, while a bitcoin splits into 100 million satoshis. The satoshi is named after Satoshi Nakamoto, the pseudonymous creator of Bitcoin.
You send a friend 50,000 satoshis and want to know the fraction of a bitcoin that is.
Convert using the fixed ratio:
50,000 / 100,000,000 = 0.0005 BTC
So 50,000 satoshis is 0.0005 BTC, the same way 50 cents is 0.50 of a dollar, just on a far finer scale.