Microsoft Azure is a cloud computing service created by Microsoft for building, testing, deploying, and managing applications and services through a global network of Microsoft-managed data centers. It provides software as a service (SaaS), platform as a service (PaaS) and infrastructure as a service (IaaS) and supports many different programming languages, tools and frameworks, including both Microsoft-specific and third-party software and systems.
Azure Storage A basic building block in any application is data storage. Azure Storage provides multiple options for storing data, like files or rows of data. It offers several different services that are all relatively inexpensive, scale almost infinitely and across geographic regions and offer features like encryption and authentication.
Web app are essential if you want to host a standard ASP.NET web application. Web Apps are an abstraction of a Web Server like IIS or Tomcat and can run applications that are written in .NET, PHP, Python, Node.js, Java and more. They are very easy to setup and provide you with lots of benefits out-of-the-box, like the fact that by default, they are available 99.95% of the time.
Office 365 is a Web-based version of Microsoft's Office suite of enterprise-grade productivity applications. Office 365 is delivered to users through the cloud and includes Exchange Online for email, SharePoint Online for collaboration, Lync Online for unified communications, and a suite of Office Web Apps, Web-based versions of the traditional Microsoft Office suite of applications.