Windows 10's Nearby Sharing feature can be easily enabled with one click in the Share dialog, but can only be disabled from the Settings app. Here's how to hide the "Looking for nearby devices" message and stop incoming share notifications.

Launch the Settings app to get started. To do so, click the Start button and click the gear-shaped Settings button (or just press Windows+I).

Click or tap the "System" category in the Settings window.

Click "Shared Experiences" in the sidebar. Click or tap the toggle button under Nearby Sharing to turn it off.

If you don't want to use Nearby Sharing with other people's PCs, but you would like to use Nearby Sharing to share content between your own PCs, there's a middle-ground option. Just click the "I can share or receive content from" dropdown and select the "My devices only" option. Nearby Sharing now will only work between PCs you've signed into with the same Microsoft account.