Web3 refers to how the Ethereum community decided that the user interface to blockchains should be web-like, instead of say via commandline terminal or via Qt desktop apps (like Bitcoin).
You can see this with Metamask, which is essentially Ethereum’s App Store for smart contracts. https://metamask.io/
From that concept, the notion extended into using crypto to augment Web2 apps, like with micropayments or NFTs or the like.
Now it is a catch-all term for the Internet of Value, or the global Web augmented with a native currency that is not controlled by any country or company.
I’m not sure it was a good idea to co-opt a familiar term (Web2.0) and then define blockchain and cryptocurrency in terms of that. It’s unsurprisingly getting pushback, and Ethereum is being accused of “marchitecture” (like with the Pentium4, tech designed for marketing which compromises true performance, or security, or something else). Blockchains are expensive fully replicated distributed databases. They inherently want to host very light weight but high-value data, like accounting ledgers or internet names, and websites and apps are not that.