Bitcoin is a digital currency which operates free of any central control or the oversight of banks or governments. Instead it relies on peer-to-peer software and cryptography.
A public ledger records all bitcoin transactions and copies are held on servers around the world. Anyone with a spare computer can set up one of these servers, known as a node. Consensus on who owns which coins is reached cryptographically across these nodes rather than relying on a central source of trust like a bank.
Every transaction is publicly broadcast to the network and shared from node to node. Every ten minutes or so these transactions are collected together by miners into a group called a block and added permanently to the blockchain. This is the definitive account book of bitcoin.
In much the same way you would keep traditional coins in a physical wallet, virtual currencies are held in digital wallets and can be accessed from client software or a range of online and hardware tools.
Bitcoins can currently be subdivided by seven decimal places: a thousandth of a bitcoin is known as a milli and a hundred millionth of a bitcoin is known as a satoshi.
In truth there is no such thing as a bitcoin or a wallet, just agreement among the network about ownership of a coin. A private key is used to prove ownership of funds to the network when making a transaction. A person could simply memorise their private key and need nothing else to