Hello,
The machine agent will be used to collect CPU / Disk / Memory stats of the server, its a standalone agent that can be restarted without effecting the application server.
The application agent will sit inside the application server and will usually stop / start with the application, it will give you loads of information regarding the health of your application server and capture the applcation transactions, allowing you to monitor such things as total login attempts and how long it took etc.
Plenty of reading here:
https://docs.appdynamics.com/display/PRO41/AppDynamics+Essentials
Jason