You need to check if the environment you are working with is cloud-only, purely on-premises or if it implements any hybrid configuration.
The hybrid environment in most cases refers to an Office 365 tenant perpetually connected with an on-premises infrastructure.
The primary feature that is being implemented in hybrid environments is the synchronization between your local Active Directory and Azure Active Directory. You can check if the synchronization is configured for your tenant by signing in to your Microsoft 365 admin center and expanding Health in the left navigation menu (Fig. 1.). If you can see Directory Sync Status in the menu, then it means that the synchronization has been set up. To determine its status, check the Directory sync enabled and Last directory sync values.
If either the link to the Directory Sync Status page is not visible in the navigation menu or the Directory sync enabled value is False, it means that your hybrid configuration in terms of Active Directory synchronization is not set up properly.
If you create objects (like users or groups) directly in your Office 365 tenant, they will not be visible to in your local AD. Instead, you need to create or edit your objects locally and synchronize the changes afterwards.
If you are running a local Exchange server environment, you can also connect it with your Office 365 tenant. This kind of deployment is usually considered a halfway point between on-premises and cloud.
To check the hybrid configuration of your Exchange, simply open the Exchange admin center and navigate to the hybrid node (Fig. 2.). If the button on the setup page says enable or configure, it means that your local Exchange is not working in a hybrid deployment.
Otherwise, if the button says modify or change, it means that your Exchange server is set up to work with your Office 365 tenant. In this case, you can use also the following cmdlet in the Exchange Management Shell (Fig. 3.) to check all features of your hybrid configuration:
Get-HybridConfiguration | fl