One Tether is the supposed to be = to one USD which is supposed to be in Tether's bank account somewhere. They have like 16 people total and are based in a mailbox in the Caribbean and nobody in the commercial paper markets have heard of them, despite them being one of the largest buyers in the world (in theory). Their "audits" aren't really audits and there's a ton of sketchiness with the firm they chose last time they ran one.
In practice they basically use their trusted position within an exchange (as the 1-to-1 representation of a US dollar) and simply create new Tethers from thin air, move them to an exchange, buy BTC, pump the price, and essentially act as a stabilizer whenever the price starts tanking. For instance they've printed over $2 Billion worth of Tether since Saturday, with absolutely no evidence that real people actually put $2B into exchanges to buy crypto.
It's an amazing scam since anytime it looks like the floor is about to fall out, they print billions more and keep their position alive by pumping crypto back up.
Anyways the reason it's important is because Tether and other stablecoins are supposed to be the fiat offramp in the event that you want to withdraw money from an exchange. After all, to buy BTC you really first bought Tether (or USDC) and then traded your tether for BTC a minute later. So all of the hard cash in the exchange is supposed to be represented by Tether... guess what happens when people realize their cash isn't actually there 1-to-1 like it was promised? Massive liquidity crises and all cryptocurrency falls 90%+.
USDC and Tether are _not_ the same thing. They're collateralized and distributed differently; the only similarity they have is being stablecoins. That's like saying potatoes and carrots are the same thing because they're vegetables.
I don't think I need to explain how risky it is to buy subprime commercial paper denominated in non-US currency to back up your USD reserves. It's not like Evergrande is teetering on the verge of a massive default or anything...
A lot of crypto trade (especially on shadier exchanges without KYC or the option to use fiat) is denominated in tether.
Tether keeps printing billions of dollars with no oversight or regulation. They lied about it being backed by cash reserves, and now make a much softer claim that its backed by "some cash" and other assets (other assets include more crypto IIRC).
Basically, it feels like tether is inflating the price of BTC, and the exchanges all have a vested interested in continuing to pretend tether is worth something. If there was a run on tether (i.e. everyone tries to exchange for fiat) it could be catastrophic for all of crypto.
(Disclaimer: I am not a financial expert, and have just picked this up from reading about tether over the last few months).
Most bitcoins are bought with tethers and tethers are issued by Tether inc. Thether inc. claims that tethers are backed by real US dollars, however nobody knows whether this is true and Tether inc. has been shown to have lied about that in the past. In short, the widespread suspicion is that exchanges and other parties are using unbacked tethers to pump the price of bitcoin up.