An analytic application is a document that can contain visualizations such as tables, charts, and filters to allow navigation and analysis of data. You can personalize the visualizations and interaction behaviors of the UI elements according to user requirements. Analytic applications are created and consumed in SAP Analytics Cloud.
With Application Design, SAP Analytics Cloud lets you create applications for data analysis and data planning. In contrast with stories, analytic applications are created by few experts, but are consumed by many end users. The Application Design environment is geared to the needs of application designers, who create analytic applications that are tailored to satisfy application users' business needs.
The major difference compared to stories is that in analytic applications, you can configure the behavior of the UI elements with a set of specific script API events, and specify which actions should take place when events are triggered. This flexibility lets you create a variety of analytic applications, ranging from simple static dashboards to highly customized analytic applications with numerous options to browse and navigate data.
Find more details about the basics here: About Application Design
As an application designer, make sure that you have got the permission for working with analytic applications. Administrators or users who can edit roles need to add the Analytic Applications permission with create, read, update and delete rights to your role.
Make sure that the users who consume your applications have got the read rights for analytic applications in their roles.