Curtain Mode is a Remote Management feature on macOS that blocks or conceals the display on the computer Screens is connected to. It's useful if you don't want the remote user to see what you're doing (e.g. entering a password or editing a sensitive system file).
This is what people in front of the remote Mac will see (the text is user-customizable).
In Screens, you will see the remote desktop.
You may enable Curtain Mode and customize the displayed text in your saved screen settings, under More Settings.
Screens for macOS
You can also toggle Curtain Mode on or off from the toolbar:
Screens for iOS
You can also toggle Curtain Mode on or off from the Actions button:
Note: This feature depends on macOS' native Remote Management service, and so is available only when connecting to a Mac.
Note that Curtain Mode may cancel any On-Disconnect Actions sent to the remote Mac.