Apple has published a technical document explaining how to back up your Apple Watch. The document notes that you don’t actually back up the watch, but rather the phone that it’s linked to. As Apple says:
“When you back up your iPhone to iCloud or iTunes, your iPhone backup will also include your Apple Watch data.”
It’s important to note that, in order to back up “Health and Fitness data, such as history, achievements, and user-entered data,” you must either back your iPhone up to iCloud, or use an encrypted iTunes backup.
To create an encrypted iTunes backup, select your device in iTunes, click Summary, and check Encrypt iPhone Backup. You’ll be prompted for a password.
If you ever need to restore this backup, you’ll have to enter the password when iTunes prompts you. It’s a good idea to do this, not only to back up your Apple Watch’s health data, but also to store passwords on your iPhone.