Hybrid deployment is a connection between your Exchange organization that is on-premises and Exchange Online. This connection is a federation that is done by Hybrid Configuration Wizard (HCW) that performs several steps:

• The configuration of SMTP connectors between Office 365 that gives the mail flow in both ways using your certificate with TLS.
• The implementation of the global address list is shared between the two organizations.
• The federation of free/busy that gives you the possibility to have the availability
  in calendars between users connected on each Exchange organization (on-premises and online).
• You can continue to use http://webmail.yourorganization.com, where you can change yourorganization.com to your public internet domain name as you did before hybrid. When a user has their mailbox moved to Office 365, it will also be connected to Office 365.
• When you have ActiveSync, the users will be automatically redirected when their mailbox moves between organizations.
• Using Exchange Web Service (EWS), you have the ability to do a remote move between your mailboxes' organizations.
• If your hybrid is Exchange 2013 or 2016, you can use your Exchange Admin center to manage both Exchange organizations.