ETH is sent to a smart contract on the Ethereum 1 mainnet. This ETH is locked away in the smart contract and doesn’t come out again.
Separately, the Ethereum 2 nodes are listening to events from the Ethereum 1 smart contract mentioned above. When it sees that someone has made a deposit it creates Ethereum 2 ETH (called BETH above) and expects the validator mentioned in the deposit contract to start validating the Ethereum 2 beacon chain.
As long as the validator does a good job validating the Ethereum 2 beacon chain the amount of BETH held for the validator increases (as the validator is given rewards for its work). At some stage the validator can decide they don’t want to validate any more, at which point they receive whatever BETH they staked plus the rewards.
(note that there are various delays and complications in place in reality, omitted for brevity).
It is worth noting that although you can swap 1 ETH for 1 BETH through the deposit contract this does not lock in the value of BETH because you cannot swap BETH to ETH. They may remain close to each other or may diverge, but there is no peg because the transfer is one-way.