Which part of Appian architecture handles the storage of relevant data for the entire application?

The correct answer is the Data Store Services. This component of Appian architecture is responsible for handling data storage, which encompasses the management of relational databases that hold application data. Data Store Services provide an interface for the application to interact with the database through queries and data structure definitions, ensuring that data is processed and accessed efficiently.

Data Store Services not only store relevant data but also facilitate connections to different data sources, allowing for a flexible integration with external databases. This enables developers to execute persistent data operations and ensure that the application's data is correctly maintained throughout its lifecycle.

The other components mentioned, while crucial to the overall application architecture, serve different roles. Appian Engines are responsible for executing application logic and processing workflow tasks. The Application Server manages the overall application, providing a platform for the web server and a place for deploying Appian applications. The Execution Engine specifically deals with the execution of rules and functions to drive business logic but does not directly handle data storage.

Thus, understanding the function of Data Store Services is essential for effective application development and data management in Appian.