Base is an optimistic rollup built on top of Ethereum. An optimistic rollup batches and compresses transactions and general computation. In an analogous manner that .zip or .tar.gz batch and compress files. The rollup executes transactions or general computation (Ethereum is a general purpose blockchain with a Turing complete programming language, so it can execute anything you code), computes a cryptographic proof of its correct execution and posting that to Ethereum. Which then verifies its correct execution.
Why do this?
Because blockchains don't scale. By don't scale I mean that there is a very explicit trade-off between vertical scalability (beefier nodes) vs. decentralization (barriers for anyone to participate in the consensus) and horizontal scalability (parallelization) vs. security (cost of attack). So Ethereum's approach to solving scalability is to accept head-on this limitation and instead of compromising on decentralization or security find ways around it.
With rollups you place the costly execution outside the blockchain and let the blockchain act as verifier and settlement layer of cryptographic proofs of computation. The blockchain verifies proofs, which are much cheaper, while the actual execution is done outside where you can scale vertically and horizontally.
With this approach Ethereum has settled over 600 bitcoin-equivalent transactions per second in the last hour (this is the actual figure, I just checked https://ethtps.info/ ). Remember when 1.5 years ago it was 15? Well... Now it's over 600. And plans to keep scaling until it reaches 1M-10M transactions per second by 2030.
So what?
Well, Coinbase is an exchange. A centralized exchange, for that matter. When you execute a transaction on Coinbase (or any other centralized exchange... NYSE, Nasdaq, Deutsche Bourse...) what knowledge do you have that the transaction was executed? That the stock the UI says you own is actually there. How do you know shorted stocks are actually lent and exist? This fixes it. You can see the code and be sure that it's executed correctly.
When CBDCs happen, and they are going to happen. The same kind of statements could be made for your money.