MAPI over HTTP is a new transport used to connect Outlook and Exchange. MAPI/HTTP was first delivered with Exchange 2013 SP1 and Outlook 2013 SP1 and begins gradually rolling out in Office 365 in May. It is the long term replacement for RPC over HTTP connectivity (commonly referred to as Outlook Anywhere). MAPI/HTTP removes the complexity of Outlook Anywhere’s dependency on the legacy RPC technology.
To learn more about this new feature, please head to : http://blogs.technet.com/b/exchange/archive/2014/05/09/outlook-connectivity-with-mapi-over-http.aspx