The Bitcoin network shares a public ledger called
blockchain. This ledger contains every transaction ever processed, allowing a user's computer to verify the validity of each transaction. The authenticity of each transaction is protected by digital signatures corresponding to sending addresses, allowing all users to have full control over sending Bitcoins from their own Bitcoin addresses.
In addition, anyone can process transactions using the computing power of specialized hardware and earn a reward in Bitcoins for this service. This is often called "mining".