The mechanism was that 1 UST (the stablecoin) is redeemable for USD$1.00 worth of LUNA (the volatile coin), at whatever the LUNA/USD exchange rate is at that point in time, and vice versa. So in theory, if LUNA was trading for $10.00 then you could exchange 1 UST for 0.1 LUNA, then sell that 0.1 LUNA on an exchange to get USD$1.00. It works in the other direction too. Arbitrage maintains that peg.

Of course, the flaw in this whole arrangement, is that if LUNA is in a death spiral and money is only really flowing out of UST/LUNA, then the peg is not maintained.

Having not looked into it, and just pulling this out of my rear, presumably the assumption would be that if it has low correlation to other cryptocurrencies, then it improves the stability of the basket of backing cryptocurrencies. Even if the correlation is high, anything less correlated than +- 1.0 helps the diversified basket.

It didn't.