A blockchain is a ledger of facts, replicated across several computers assembled in a peer-to-peer network. Facts can be anything from monetary transactions to content signature. Members of the network are anonymous individuals called nodes.
All communication inside the network takes advantage of cryptography to securely identify the sender and the receiver. When a node wants to add a fact to the ledger, a consensus forms in the network to determine where this fact should appear in the ledger; this consensus is called a block.
Mining blocks by changing the nounce of a block until it's hash is below a "difficulty" hash. E.g.
hash(block + nounce) < 00010000.
The more computing power a miner has, the more likely they are to find a valid block. Downsides:
Forging blocks by providing stake (currency). Forgers are rewarded for their stake, if a block includes a fraudulent transaction, they loose stake.
It's possible to be come a stakeholder (called validator in Ethereum 2.0) and earn on the rewards.