ArcGIS Server is a technology that allows you to pull your heavy work load on the backend and isolate the clients from complexity of the database by exposing HTTP services instead of low level TCP database. You can also extend the server capability by writing your own extensions. 
In this episode ArcGIS Server talk we will talk about two ways you can extend your ArcGIS server, Server Object Extensions and Server Object Interceptors.
Server Object Extension 
Extends the MapServer to allow you to write your own logic that cannot be easily done by built - in Feature Server or Map server. Or it is more performant to do it.  
Users create new excavation I want to auto-calculate the price of the excavation based on the soil type, whether there are trees, rocks. 
Server Object Interceptors 
You don’t write new thing you instead intercept existing calls to query and applyEdits to inject your own logic to pre or post processing. Lets say every-time any application tries to write to the service, you want to verify that the edit is permissible. Include water marks to all images that are downloaded.
Learn more about SOE vs SOI here
http://enterprise.arcgis.com/en/server/latest/publish-services/linux/about-extending-services.htm