SQRL (pronounced "squirrel") stands for (S)ecure (Q)uick (R)eliable (L)ogin. It is a new login technology meant to eliminate many of the common issues we currently experience with traditional username and password style logins. It is extremely simple to use and completely secure.
When a user wants to log in to a website, they will typically be presented with a login form consisting of a username and password. The user will enter their information into the browser, click on login and they are logged in to the website.
By logging in this way, the user must trust both the website to store their username and password and not lose it (via hackers or other means), and they also must trust the computer and browser they are logging in with no to leak their credentials either.
Now enter SQRL: the user sees the same login page, but now it has a SQRL QR code next to the login. If the computer has a SQRL client installed with the user's identity, they can just click on the QR code and the user is logged in. If the computer is not a trusted one, or does not have a SQRL client installed, then the user can pull out their mobile device, snap a picture of the QR code using their SQRL client and click on the log in button. That's it. The user is now securely logged in to the website without providing any sensitive information to either the computer, browser, or website!