In a Lync hybrid deployment, we have the following:
User accounts and related information homed in the on-premises Directory Services and replicated to Office 365.
A part of our Lync users that consume on-premises resources and a part of them that use online (Office 365 / Lync Online) resources.
The same (public) domain name used both online and on-premises (Lync-split DNS).
Other Office 365 services and integration with other applications available to all our users, irrespective of where their Lync is provisioned.
One way to define Lync hybrid configuration is by using an on-premises Lync deployment federated with an Office 365 / Lync Online tenant subscription. While it is not a perfect explanation, it gives us an idea of the scenario we are talking about. Not all the features of Lync Server 2013 (especially the ones related to Enterprise Voice) are available to Lync Online users. The previously mentioned motivations, along with others (due to company policies...