Working on a project from start to finish, sitting in on meetings and presentations with our client knowing that I'd contributed to the final result. Gave me a great perspective on both how normal businesses operate, but also on how a normal consulting job works.
In the beginning (particularly the first week) I was given very little to do, which is both dull and frustrating.
Advice to Potential Interns
They get their interns involved, good, friendly office atmosphere, work can be quite interesting.
Advice to Management
Just make sure from day 1 that there is a plan in place for the interns (maybe training the first couple of days, before assignment to a project).