4. Proof of work
For Bitcoin to work, it needs a way to validate transactions and timestamp them. It does that with a proof-of-work system.
As mentioned in the section above, every block of transactions has a hash associated with it. In Bitcoin's proof-of-work system, network nodes, or miners, compete to complete a block with a unique number called a nonce in such a way that the block's hashed value is lower than a targeted hash value. The difficulty of guessing a hash that is lower than the targeted hash value is adjustable to achieve the desired number of average blocks per hour. Finding the correct value satisfies the requirements of proof of work because it demonstrates that the nodes have expended computing power.
As the Bitcoin white paper describes it, this is essentially a one-CPU, one-vote system. If honest nodes control a majority of the CPU power, then there will be an accurate, honest blockchain.
5. Network
On the Bitcoin network, transactions are broadcast to every node. Each node collects new transactions into a block. Then it works on finding the correct hash value for the block to satisfy the proof-of-work requirement. Once a node does that, it broadcasts the block to all nodes.
If all the transactions in that block are valid, then nodes accept it and move on to start trying to mine the following block on that chain. They show they've accepted it by adding it to the system and beginning work on the next block of transactions. Nodes always consider the longest chain to be the correct one. This is important because in the rare event of a "tie," miners could end up working on two alternate forks. However, as soon as one of them is successful at adding the next block, it will become the longest chain, and all nodes will then recognize it as the definitive blockchain.
6. Incentive
Nodes are the backbone of the Bitcoin network. To encourage honest participation, the system has a built-in reward for the creator of each block. The creator is the node that first solved a block's proof-of-work requirement and broadcast it to the other nodes.
The first transaction in a new block issues a new coin to the creator of that block. The block reward can be funded by newly minted coins, making it a way to introduce more coins into circulation. It can also be funded with transaction fees. In fact, after the full supply of Bitcoin has been mined in the future, mining rewards will come solely from transaction fees.
7. Reclaiming disk space
Older Bitcoin transactions can be hashed into a Merkle Tree. A Merkle Tree saves space by using a summary hash of multiple transaction hashes and freeing nodes from having to refer to them all individually to validate past transactions. Simply put, this allows older blocks of transactions to be compacted, reducing the amount of storage required for the blockchain.