Centralized Mail Flow
Centralized Mail Flow enables all outbound messages from both organizations to be routed through the on-premises organization. This allows for additional processing by on-premises message hygiene or compliance solutions.
Non-centralized Mail Flow
Non-centralized Mail Flow is selected by default in the Hybrid Configuration Wizard; Office 365 sends messages directly to the Internet and the on-premises organization continues to send messages as configured before. Alternatively, you can configure the on-premises organization to route all outbound email through Exchange