Windows 10 can synchronise notifications across your devices, letting you get notified about text messages and app alerts from your phone on your PC. The system relies on Cortana to keep notifications updated in the cloud. You can control the feature and change the apps that are synced, although the settings aren't where you may expect them to be.
Most of Windows 10's notification settings are accessed from the Settings app. Sync options are a special case though. Because they're controlled by Microsoft's digital assistant, you have to use the Cortana's UI to adjust how sync works. While this fragmentation isn't convenient, it does ensure there's a consistent place to access sync settings if you're using the Cortana app on an iOS or Android device.
Provided you have the Cortana app installed on your phone, and you're logged in to the same Microsoft Account on both the phone app and your PC, you should see your mobile notifications appear on your PC a few seconds after they arrive. To change the apps that you get notifications from, launch Cortana on your PC. Click the cog icon in the bottom-left corner to open the Settings menu and scroll down to the "Send notifications and information between devices" section. Click the "Edit sync settings" button to adjust how sync works.
On this page, you'll see three different options, if sync is enabled. "Get notifications from this PC on my phone" and "Upload notifications from this PC to the cloud" control whether notifications you receive on your desktop should be synchronised to your other devices. These are simple on or options you can change by clicking on the setting and then the toggle button that appears.
The other item in the menu, "Mobile Device," controls how notifications from your phone should be displayed. Tapping the category will open the Mobile Device settings page. At the top of the section, you'll see a global toggle button that lets you turn off mobile notifications entirely. Below it, you'll see a list of apps from your phone that have displayed notifications on your PC. You can use the toggles to control whether each app can continue to send alerts in the future.
If you're on your phone, you can use the same screen to define which apps upload notifications to the cloud. This has a subtle difference to the menu on PC. If you disable an app while on your phone, none of your other devices will receive notifications from it. If you leave it turned on but block it in your PC's settings, only that device will be affected.
These settings let you control which cross-device notifications you receive and configure how devices should display them. Although the options aren't especially visible or user-friendly, they give you the ability to synchronise notifications while excluding mobile apps you may already have installed on your PC. If you'd rather not use the functionality, you can turn it off entirely with the toggle button above the "Edit sync settings" button on Cortana's main settings page.