watchOS 3.1.1 can be downloaded through the dedicated Apple Watch app on the iPhone by going to General --> Software Update. To install the update, the Apple Watch must have 50 percent battery, it must be placed on the charger, and it must be in range of the iPhone. watchOS 3.1 requires an iPhone running iOS 10 to install.
As a minor 3.1.x update, watchOS 3.1.1 appears to focus on under-the-hood bug fixes and performance improvements, with no outward-facing changes discovered in the first watchOS 3.1.1 beta. We'll update this post should any new features be discovered in the second watchOS 3.1.1 beta.
watchOS 3 completely overhauls the interface on the Apple Watch, introducing a dedicated app dock, instant launch apps, new watch faces, and new complication options. There are new Activity sharing features, a "Breathe" app guides users through deep breathing sessions to cut down on stress, and an SOS feature can automatically call emergency service.
For more details on what's new in watchOS 3, make sure to check out our watchOS 3 roundup.