Google Merchant Center
The Google Merchant Center is a tool that helps you upload your store and product data to Google and make them available for Google Shopping campaigns and other Google services.
Shopify's Google Shopping channel asks you to log in to your Google account to sync your Shopify store with your Google Merchant Center account. If you don't already have a Google Merchant Center account, then an account is created for you during setup.
Syncing your Google Merchant Center account
When you set up the Google Shopping channel, Shopify syncs your products and relevant Shopify store settings like shipping and taxes to the Google Merchant Center.
Syncing your domain
Each Google Merchant Center account needs to be associated with a verified domain that isn't associated with another account. To set up the Google Shopping channel, your Shopify store's domain needs to be claimed, which means it's reserved for use with the Google Merchant Center account that you added to the channel.
When you're setting up a new or existing Google Merchant Center account with the Google Shopping channel, your Shopify store's domain is claimed automatically unless it's associated with a different Google account. If your domain is associated with a different Google account, then you need to claim the domain for the account that you want to use with the Google Shopping channel, and it won't be available for use with another Google Merchant Center account.
You can read more about verifying and claiming your domain from Google Merchant Center Help.
Syncing your product feed
The Google Shopping channel syncs your products in a separate step after your Merchant Center Account has been configured. If you already have a product feed set up, then it is overwritten to avoid conflicts between your Shopify store and your Merchant Center account. For more information about managing which products are synced, see Syncing your products.