DAI is a complex series of loans, borrowing, and interest that creates incentive to sell your DAI if it goes over $1 and incentive to buy if it goes below $1. DAI has basically maintained $1 for years even as ETH prices have been all over the place. It's battle tested. If you can't be bothered to do a few minutes of research on a complicated topic I don't know what you're doing here.
So far, I have a 20-minute video that is clearly mostly not about the Dai peg, and a link to a very wordy "paper". I skimmed both, and the answer is apparently "oracles", or a price feed from several crypto exchanges. That's a really simple answer, that doesn't need burying in layers of cryptobabble and an attitude that I can only describe as condescending.
It is very good to be critical about the value of information others provide.
But I find your commenting style abrasive; I wouldn't be surprised to see you flagged if you continue with it (especially with multiple examples in a single thread). Occasional outbursts seem to be tolerated here, although frowned upon as unconstructive. I myself personally tend towards abrasive confrontation of facts; but I really value the rules here since they create good discourse and avoid discord.