watchOS 9.3.1 can be downloaded for free through the Apple Watch app on the iPhone by opening it up and 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.
According to Apple's notes, watchOS 9.3.1 adds "bug fixes and important security updates" to the Apple Watch.