The feature, called Smart Lock, uses Bluetooth to connect a Chromebook with any phone running Android 5.0 Lollipop. When the devices are paired, and the phone is unlocked, users can log into their laptops just by pressing a button.
Google announced Smart Lock way back at its I/O developer conference in mid-2014, but the feature didn't show up in the developer version of Chrome OS until last December. Now it's available in the stable version (though very few devices are running Android 5.0 at the moment).
To set it up, click your account picture in the status area (lower-right corner of the main screen), then head to Settings > Show advanced settings. Click Set up under the Smart Lock section, and follow the on-screen instructions.
Smart Lock works only if your Android phone is unlocked, and constantly fishing your phone out of your pocket could be more trouble than it's worth. Fortunately, Google offers a separate Smart Lock feature for Android that keeps the phone unlocked when it's in a trusted location (such as your house) or paired with a trusted Bluetooth devices (such as your smartwatch). You can set that up through the instructions on Google's website.
Why this matters: Chromebooks are supposed to be all about speed, yet entering a password to access your account has always been mandatory. Though Smart Lock takes a bit of setup, it should be a huge timesaver for Chromebook users in the long run.