You are describing Activation Lock, which prevents unauthorised use of Apple Watch if it is lost or stolen.
If the Apple Watch is locked to your own account, but you are having issues with your credentials, then it may help to follow the instructions here:
Otherwise, follow the steps here to remove the lock:
If you still need assistance, contact Apple Support or make a Genius Bar reservation, taking along your Apple Watch, proof of identity and your original proof of purchase for your watch:
- US: Apple Watch Service Answer Center - Apple Support
- Elsewhere: Select your country for Apple Watch service and repair information
If the Apple Watch is instead pre-owned and locked to the previous owner's account:
- You will need the previous owner (who may not be the seller) to either enter their Apple ID and password on your iPhone or to turn the feature off via https://www.icloud.com/ (by signing in with their Apple ID > Find My iPhone > All Devices, then select the Apple Watch > Erase Apple Watch > Next until erased > click X next to the watch).
- If you cannot arrange for the previous owner to do this, then you should return the watch for a refund.
- You will not otherwise be able to use the watch. There is no way around this security feature.
- Apple will not advise you of the previous owner's contact details, nor will Apple pass your details on to them.