What is the "akd" process, and do I need to allow it to connect to the internet?

Little Snitch Research Assistant tells you what it is.

akd is part of the AuthKit (authentication/authorisation) framework. Also used in the process of authenticating of iCloud and other accounts using Apple ID.

Googling for scraps of info, I can't find anything complete, but it appears to be the Auth Kit daemon. A daemon that handles authentication needs of the OS.

According to Know your Mac OS X processes at Triviaware it's located at
/System/Library/PrivateFrameworks/AuthKit.framework/Versions/A/Support/akd

Comments below imply that it is new to El Capitan & is used to authenticate the App Store. App Store login fails if you block it.