Very much a dabbler myself, and I'm not going to pretend I know a ton about this stuff either but:
The idea is to represent ownership of stocks as tokens on a blockchain. You could either back the tokens 1:1 with real shares held in custody (like stablecoins are backed by fiat), or a company could simply issue its shares directly on the blockchain as digital tokens. So if Apple (for example) launched a new class of stock, instead of listing it on Nasdaq and keeping the shareholder ledger with a transfer agent, it could just issue tokenized shares on (say) Avalanche. The tokens would represent real equity in Apple, with dividend rights, voting rights, etc. All shareholder transactions happen on chain, visible to anyone, and settle instantly.
It's actually way simpler than it sounds. The whole idea of "stocks" and the "stock market" is way, way more complicated than companies simply issuing tokens on a blockchain directly to purchasers. Not only is it way more transparent, but it eliminates a whole lot of middle men (mostly).
You can get global capital access, instant settlement, smart contract automation (dividends, voting, splits could be automated), transparency, and low issuance costs (especially for startups). Huge benefits for everyone involved.
FWIW, I have no idea why anyone would bother with the first option- the whole 1:1 tokens backed by real stock stuff. Makes zero sense. Just bypass that step entirely and use tokens.
I came across the article 3 or 4 years ago
Cryptocurrencies Won't Replace Currencies: They Will Replace Stock Exchanges and actually mentioned the idea in this very thread. I got totally shit on lol. But here we are years later and it looks like it's happening.