Provider hosted app helps to run the custom code (Example CSOM.Net) outside of your SharePoint farm. In case of Office 365 you cannot have custom code so you need to host provider hosted app in your own infrastructure.
One of the examples of provider hosted app is developing remote event receivers.
http://www.sharepointnutsandbolts.com/2013/07/deploying-sp2013-provider-hosted.html
One best option we have is host, the provider hosted app in Azure, which you have already tested.
My Blog- http://www.sharepoint-journey.com|
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