Backtracking a bit, let's talk about "nodes." A node is a powerful computer that runs the bitcoin software and helps to keep bitcoin running by participating in the relay of information. Anyone can run a node, you just download the bitcoin software (free) and leave a certain port open (the drawback is that it consumes energy and storage space – the network at time of writing takes up about 145GB). Nodes spread bitcoin transactions around the network. One node will send information to a few nodes that it knows, who will relay the information to nodes that they know, etc. That way it ends up getting around the whole network pretty quickly.
If Eve offers to pay Alice a bitcoin in exchange for goods and signs a corresponding transaction, it is still possible that she also creates a different transaction at the same time sending the same bitcoin to Bob. By the rules, the network accepts only one of the transactions. This is called a race attack, since there is a race which transaction will be accepted first. Alice can reduce the risk of race attack stipulating that she will not deliver the goods until Eve's payment to Alice appears in the blockchain.
Requiring a proof of work to accept a new block to the blockchain was Satoshi Nakamoto's key innovation. The mining process involves identifying a block that, when hashed twice with SHA-256, yields a number smaller than the given difficulty target. While the average work required increases in inverse proportion to the difficulty target, a hash can always be verified by executing a single round of double SHA-256.
Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented by an unknown person or group of people using the name Satoshi Nakamoto and released as open-source software in 2009. Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies, products, and services. Research produced by the University of Cambridge estimates that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.