What are the services Apple's Firewall considers essential?
Essential services are those in the Core Services layer. When that option is checked, only the incoming connections to the below services will be allowed:

From https://developer.apple.com/library/mac/documentation/MacOSX/Conceptual/OSX_Technology_Overview/CoreServicesLayer/CoreServicesLayer.html


  The technologies in the Core Services layer are called core services because they provide essential services to apps but have no direct bearing on the app’s user interface.


Some of the notable core services are 


accounts &amp; Social media integration
identity service
time machine
keychain services
notifications
iCloud storage
cloudkit
file coordination
bundles and packages
internalization/localization
bonjour
security services
address book


And from http://www.macworld.com/article/1131116/firewall.html#configure


  The second option, “Allow only essential services,” will block anything except a few default services that support networking, such as Bonjour. Only use this option if you want to block everything; this will prevent any file sharing, remote access, or other services activated elsewhere on your Mac. 


You can switch your firewall settings and run nettop in Terminal to monitor the network activity of each process that is running.