AD synchronization between the on-premises and Office 365 organizations is performed every 30 minutes by a server on your on-premises, running Azure AD Connect, and it is a requirement for configuring a hybrid deployment.
To know about certificates, bandwidth, mail flow, and information rights management, refer to https://technet.microsoft.com/en-us/library/mt595771(v=exchg.150).aspx.
It is advised that you always review all the requirements before starting.