You send your ETH to a specific contract, from which it can't be moved (whether you want to call that "burning" is up to you, but it's probably a bit confusing). Each validator must also run an Eth full node, and uses the state of that contract to determine who can act as a validator on the Beacon chain.
Not OP, but I can give some elaboration on why Cardano is a really interesting project:
1. Staking in Cardano does not lock up your funds, and is really decentralized, getting more every day. Because of that, more than 70% of all coins are currently staked. This brings less volatility to the price and ensure longevity of the chain. The interest is not too big too, everything seems as sustainable as it can be.
2. Cardano supports assets natively instead of having them just being backed by smart contracts (this is/will be still possible though), which means that there are no extra gas fees to send/receive stablecoins or assets other than Ada.
3. Babel fees are part of 2, it means that the transaction fees can be paid by native tokens, not only ada. This is a huge improvement from the BSC or Eth, where you need BNB/ETH to pay transaction fees even if you're only dealing in stablecoins.
4. Smart contracts are finally coming in Q2, which will bring DeFi to Cardano (this explains the price mooning in late feb, early march, because of the mary hardfork).
5. Forks and updates in the chain are painless, last one I didn't even had to send money to a new wallet or anything like that.
6. New developments and features to the chain and ecosystem are being "baked into the protocol", in a sense. Project Catalyst is the first step for this, financing some projects, but in their roadmap they plan on giving away all control of the direction of the coin, and only work as a service provider to the ecosystem using the same infrastructure as all the other projects.
I'm really bullish on this coin, not only on price but also on the kinds of problems it can solve. Can answer more questions if you have any :)
