Proofing in Capture One allows you to get an impression of how your image will look in its final form. For instance, if you are working with an image that you want to print in grayscale you can soft proof it in Capture One, which means that by selecting a working space destination you will be able to see the image on screen in the selected grayscale profile.
In the Windows version of Capture One you can set up your soft proofing from the Color Management Settings from the Workflow menu.
Set your Output destination (Working Space) profile to the desired profile (e.g. grayscale) this way the preview of your image will automatically be updated to the desired profile.
In the Mac version of Capture One you can set up the profile from the Image>Proof menu.
Alternatively you can select it in your process settings (if you have set up your process destination to be “Selected destination")