The short of it is:
- The block chain is a distributed ledger database, where all peers hold a full copy to avoid manipulation (faking an entry is only possible by controlling >50% of machines in this peer-to-peer network).
- Spending money is implemented by adding a transactional record to the blockchain ledger at the end saying X amount moved from account A to B. A block is like a page in a paper ledger and they are appended with cryptographic hashes to avoid improper interference.
- Ethereum supports smart contracts, which are little scripts in a language called Solidity. So you can implement legally binding (and unstoppable) contracts along the lines of "if (condition) then (pay some money to someone)". Executing smart contracts cost a little bit of money. All Ethereum nodes collectively implement a distributed VM, and that money (called "gas") is the incentive to keep the network running. Smart contracts are highly interesting, and they have applications far beyond electronic currencies. For example, we played with implementing electronic rights management (https://link.springer.com/chapter/10.1007/978-3-030-36691-9_... - which turned out to be less than ideal due to a stack size limit in the current Ethereum VM, but hey).
- Whenever a new block (page in the ledger) needs to be created because the previous one is full, a randomized alg. determines who is permitted to do that ("mining"). The old process (proof of work) was environmentally a disaster (it still is for the Bitcoin ecosystem), which is why the Ethereum people implemented a smarter method (proof of stake - https://en.wikipedia.org/wiki/Proof_of_stake).
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