It was a system built on sleight of hand, with a cover story just complex enough that it worked for a while.
How do you create a stablecoin? There are two ways in general. One is to have it backed 1:1 with a bank account somewhere that contains the actual currency it represents. In theory you then allow people to freely exchange back and forth between tokens and dollars. Tether kinda/sort works this way in theory.
The other way is to play games with algorithms and try to use the market against itself to create stability. Terra (UST) attempted to do this by running a complex scheme that leveraged a floating backing token, Luna, and a smart contract which allowed you to exchange 1 UST for $1 worth of newly created Luna. If UST starts to lose its peg and become worth less than a dollar, people buy it to exchange for $1 worth of Luna, sell the Luna for a profit, so arbitrage sorts the price out. If it becomes worth more than a dollar, you buy Luna, burn it to convert to new UST, then sell that for a profit, adding sell pressure and diluting the supply.
Even with the best will in the world systems like this could best be described as meta-stable, i.e. it'll smooth out minor perturbations but there are limits.
One major problem is how do you get Luna to be worth anything though? Well you offer inducements like a ridiculous interest rate, high enough that anyone outside the cryptocurrency bubble would immediately see a red flag, and which then has to be subsidised by ... creating more tokens.
Eventually the limit was discovered, Luna dumped massively and the whole illusion collapsed.