Azure App Service is a one-of-a-kind cloud service which allows developers to easily build employee, partner and customer-facing apps for any platform or device.
It is an integrated solution that streamlines development while enabling easy integration with on-premises and SaaS systems while providing the ability to quickly automate business processes.
Azure App Service brings together the capabilities from Azure Websites, Azure Mobile Services, and Azure BizTalk Services into a unique integrated offering, while adding powerful new features. App Service includes the following app types:
Web Apps: Create mission critical Web apps that scale with your business.
Mobile Apps: Engage employees, partners and customers on any device at any time.
Logic Apps: Automate business processes across SaaS and on-premises.
API Apps: Easily build and consume Cloud APIs within any app.
For more information read Microsoft's official announcement.