Tether is a token used to trade cryptocurrency with. The CEO of Tether is also the CEO of BitFinex, the largest crypto exchange in the world. Tethers are supposed to be backed by USD. So, for every Tether they issue, they have a dollar in their bank account. Everytime a new bunch of Tethers is 'created', the price of Bitcoin shoots up, because they buy Bitcoin with it on Bitfinex. Because they are issuing so many Tethers (100 million in a day isn't uncommon), people are starting to doubt whether they actually have the USD to back it.
To be fair, Friedman LLP did release a statement about Tether. They verified that banks were held in Tether's name in the amounts of outstanding USDT. They couldn't technically verify Bitfinex's access to the accounts or other obligations, but I don't think we should assume insolvency. They are rightly worried about regulatory action and are in a serious pickle, but that's a different discussion.
Also, I've been watching the exchange price action closely. Coinbase/GDAX has been leading Bitfinex significantly during upward spikes, suggesting that it isn't Tether that's pumping the price. And if you look at Tether's circulating supply, it's silly to think it could singlehandedly prop up the entire market.