Bitcoin

Bitcoin is a payment mode invented by a Japanese, Satoshi Nakamoto in 2008. He later published its open source software in 2009.

This system is such that peer to peer users can transact directly without any intermediary. Transactions are verified by network nodes and recorded in a public distributed ledger called the block chain.
The ledger uses bitcoin as an unit of account. It is considered by the United States Treasury as a decentralized virtual currency. Bitcoin is often considered as the first cryptocurrency.

Bitcoins are created as a reward for payment processing work in which users offer their computing power to verify and record payments into a public ledger. This activity is called mining and miners are rewarded with transaction fees and newly created bitcoins.

A lot of merchants are increasingly accepting  bitcoins as a mode of payment.

As directly quoting Wikipedia,

Units

The unit of account of the bitcoin system is bitcoin. As of 2014, symbols used to represent bitcoin are BTC, XBT. Small amounts of bitcoin used as alternative units are millibitcoin (mBTC), microbitcoin (µBTC), and satoshi. Named in homage to bitcoin's creator, asatoshi is the smallest amount within bitcoin representing 0.00000001 bitcoin, one hundred millionth of a bitcoin. A millibitcoin equals to 0.001 bitcoin, which is one thousandth of bitcoin. One microbitcoin equals to 0.000001 bitcoin, which is one millionth of bitcoin. A microbitcoin is sometimes referred to as a bit.