For those that are unaware, Dai is a decentralized stable coin that lives 100% on-chain with no 3rd party custody.
Unlike Tether you don't have to trust they are solvent, you don't have to trust them to not exit scam, you don't have to trust the local government not to freeze their account.
Dai is not backed 1:1 with the USD, Dai is backed 1:1.5 with USD (in Ether).
It basically works by someone locking up their Ether in a smart contract, and then you are able to draw Dai against your Ether. If your collateral is ever less than 150% of the Dai you've drawn then you get liquidated and your Dai is repaid by someone who bought your Ether. It is this mechanism which ensures Dai is always backed by real value.
CDPs (the smart contract to draw Dai) allow you to borrow money from yourself! The best part is, the thing you borrow is a fully backed stablecoin pegged to the USD!
It's the best thing to happen to Bitcoin since Ethereum in my opinion.
A stable, decentralized, permissionless p2p cryptocurrency is what Bitcoin's original mission was all about! It basically takes the best part of Bitcoin but removes the volatility, which is a major barrier to global adoption.
Don't take my word for it, please check out this link which has dozens of articles, explanations, critiques, refutations of critiques, and other documentation that can let you make up your own mind that this is as cool as I am saying.
Let me know if you have any questions I'm always happy to chat about Dai.
Edit: I highly recommend you go over to http://cdp.makerdao.com and try out the system for yourself! All you need is a Metamask account (chrome browser extension) and some ETH. It's incredible.
Edit 2: This is a great high level overview of Dai given from a talk by MakerDao's Andy Milenius. Highly recommend!
Edit 3: I have to give a shoutout to Austin Griffith and the burner wallet! It's an awesome browser based wallet that uses the xDai side chain to have instant transactions in Dai. Try it out on your phone browser at http://xDai.io The idea is that you accept or pay in small amounts (less than $50) and at the end of the day sweep the funds into cold storage. It's called a burner wallet because when you're done you burn the private key and it generates a new burner wallet right away. It's super cool. It's run on a 'Proof of Authority' network with several respected teams in the Ethereum space, so it's centralized, but the idea is you only use it as a hot wallet for small amounts.