"Innovations are always ahead in the game" in terms of Microsoft, to support this, our well known OWA (Outlook Web Access) is renamed, rather I would say reborn with set of additional features as "Outlook on the web".
As the technology advancements are made at one side in the world of Microsoft, simultaneously the name changes Windows Azure became Microsoft Azure, then Sky Drive to One Drive, recently Lync to Skype for Business and the subsequent Online versions got their new names etc.
Office 365 is the first place where you will get the new features, If you have enabled first release program for your tenant, then you would get this new experience in first place as the name implies on the fly.
Outlook on the web comes with lot of new features as stated in the Official blog post and the experience will get better over time. As we all know that with Office 365, Outlook Web Access is the prominent or recommended client to access the service and to emphasize this we can see more new enhancements made to the UI and other key areas that makes this stand ahead the traditional Desktop client at various instances.
This naming convention will be the same when you deploy Exchange Server VNext i.e. Exchange Server 2016 as explained in the EHLO blog post.
Review the Official blog post here: New features coming to Outlook on the web