1. The Blockchain is a register or database containing statements (e.g. ownership, rights or a smart contract) provided by the participants to provide a complete history. The history cannot be modified or deleted you can only add new statements
The Bitcoin Blockchain contains statements of change of ownership - the first statement of a bitcoin ownership is the coinbase transaction inherent in each new Block (currently 25 new bitcoins per Block awarded to the validator)
2. There are rules defined for a particular Blockchain that determine what statements and in what form can be added to a Block
The Bitcoin rules require the current ownership to be checked and the correctness of the digital signature (elliptic curve cryptography) provided by the owner to transfer ownership
3. The Block validator for each new statement checks the rules have been obeyed
In Bitcoin the validator is the community of miners, themselves constructed as pools or farms to get maximum processing capability
4. The Validator validates the Block and links it to the chain using hash functions in exchange for a reward
The Bitcoin reward to the validator or miner is currently 25 bitcoins per block validated but this will halve every 210,000 blocks (about 4 years) until 21m (arbitrary limit) bitcoins have been issued in about 2140. A bitcoin is currently worth $277
5. The Blockchain may be public (accessible to all) or private (accessible to the membership)
The Bitcoin Blockchain is public
6. The Blockchain may be centralised (validated by an entity) or decentralised (validated by a community)
The Bitcoin Blockchain is decentralised
7. A validation community has to reach consensus to validate a Block, an entity has intrinsic consensus
The Bitcoin consensus is reached by miners calculating a hash function (SHA256 applied twice) of the new block including a link to the existing blockchain with certain properties, it currently takes on average 10 minutes, and this Proof Of Work (POW) is manipulated every 2016 blocks (about 2 weeks) to always take about 10 minutes on average. The cost of mining (currently about $300m per year) is barely covered by the reward of bitcoins (currently about 1.3m X current value = $360m per year). Transaction fees are currently optional.
Management of the Bitcoin Blockchain by the validators doesn't require secret cryptographic keys which is not only necessary because of the problems of trusting an open community but it is also a very smart part of the security design.
8. The Blockchain may be permissioned (users have identity) or permissionless (users are anonymous or pseudo-anonymous)
Bitcoin is permissionless, the participants are pseudo-anonymous - they are associated with one or more digital addresses representing the bitcoin ownership which could allow some forms of tracking depending on how they are used.