On Mac OS 10.15 Catalina or later, you need to allow Zoom access to screen recording to share your screen. You can do this in your System Preferences > Security & Privacy > Privacy > Screen Recording. Check the option for zoom.us.
If you have Zoom installed but you don't see Zoom in the Screen Recording Privacy options, you first may have to launch Zoom and then attempt to share your screen and use the screen recording function. This will then prompt the ability to allow access in the Security and Privacy settings.
For more information on screen sharing, check out this link on the Zoom Help Centre: https://support.zoom.us/hc/en-us/articles/201362153-Sharing-your-screen-content-or-second-camera