Computing power is often bundled together or "pooled" to reduce variance in miner income. Individual mining rigs often have to wait for long periods to confirm a block of transactions and receive payment. In a pool, all participating miners get paid every time a participating server solves a block. This payment depends on the amount of work an individual miner contributed to help find that block.
The proof-of-work system, alongside the chaining of blocks, makes modifications of the blockchain extremely hard, as an attacker must modify all subsequent blocks in order for the modifications of one block to be accepted. As new blocks are mined all the time, the difficulty of modifying a block increases as time passes and the number of subsequent blocks (also called confirmations of the given block) increases.
The whole process is pretty simple and organized: Bitcoin holders are able to transfer bitcoins via a peer-to-peer network. These transfers are tracked on the “blockchain,” commonly referred to as a giant ledger. This ledger records every bitcoin transaction ever made. Each “block” in the blockchain is built up of a data structure based on encrypted Merkle Trees. This is particularly useful for detecting fraud or corrupted files. If a single file in a chain is corrupt or fraudulent, the blockchain prevents it from damaging the rest of the ledger.
Bitcoin is the first cryptocurrency, a concept that was discussed in the late 90s. The first Bitcoin specification and proof of concept was published in 2009 in a cryptography mailing list. The concept was presented by a person or group known as Satoshi Nakamoto. The real identity of Nakamoto has been a mystery since that time, with various theories on who the individual or group may be.
During mining, your Bitcoin mining hardware runs a cryptographic hashing function (two rounds of SHA256) on what is called a block header. For each new hash that is tried, the mining software will use a different number as the random element of the block header, this number is called the nonce. Depending on the nonce and what else is in the block the hashing function will yield a hash which looks something like this:
Bitcoin's origin story sounds like something out of science fiction: It was launched in 2008 on the heels of a white paper published by the mysterious Satoshi Nakamoto, whose real identity – and country of origin – are unknown. Nakamoto conceived of Bitcoin as a currency that was 1) encrypted; 2) decentralized, i.e. it was ungoverned and did not belong to any nation; and 3) a digital "distributed ledger," such that everyone can verify online the legitimacy of transactions.
You can buy bitcoins at online exchanges similar to a paypal account. Companies like Coinbase allow you to buy bitcoin with a credit card along with wire transfers, checks and ACH. You can also use professional exchanges like Coinbase Pro that allow for institutional investors and experienced traders to trade in high volumes in a variety of cryptocurrencies with minimal fees.