watchOS 4.3.1 can be downloaded through the dedicated Apple Watch app on the iPhone by going to General --> Software Update. To install the new software, the Apple Watch needs to have at least 50 percent battery, it needs to be placed on a charger, and it needs to be in range of the iPhone.
As a 4.x.x update, watchOS 4.3.1 is minor in scale, focusing primarily on bug fixes and other under-the-hood performance improvements, with no major feature changes discovered during the beta testing period.
Prior to the release of watchOS 4.3.1, Apple stopped letting developers update Apple Watch apps built on the original watchOS 1 SDK. Starting with watchOS 4.3.1, you'll see an alert when launching a watchOS 1 app warning you that the app may not be compatible with future versions of watchOS.
This warning suggests Apple will perhaps drop support for watchOS 1 apps entirely in the future, perhaps in the upcoming watchOS 5 update that Apple will unveil at the Worldwide Developers Conference next week.
According to Apple's release notes, the watchOS 4.3.1 update also fixes a bug that could cause the Apple Watch to sometimes remain at the Apple Logo during startup for some users.