What is Azure Active Director? and of course they have exact same title article covering exactly I wanted to know at https://azure.microsoft.com/en-us/documentation/articles/active-directory-whatis/. So here is my short memo version.
Azure Active Directory is a service where you can manage things around credentials. You can offer your app, API and other services based on credentials that you manage on Azure Active Directory.
For example, you have API service that is privately offering and want to manage accesses, you can do so through Azure Active Directory.