To add product data in the product editor, first pick an item in the All Products page or create a new one. In the Google section, a Category needs to be entered to turn the red X into a green check mark by the channel name. The category can be added by either searching by name with the Category field or directly entering the Category ID in the Category ID field. If a category is selected by searching in the Category field, then the Category ID will populate in the Category ID field:
To learn more about product requirements for Google, please see the Google Feed Troubleshooting Guide
The available values for Category / Category ID can be retrieved from Google or are available from their taxonomy here.