As an audit intern with Deloitte, I worked in the middle of audits as if I was a full-time employee. The team had me working on workpapers and asking questions to the client when necessary. I was able to really be a part of the team working towards completing the audit. When I completed my internship, I had a very good picture what it would be like to be a full-time employee with the company.
Honestly, very little from an audit intern perspective within the role of your engagement. However, being selected as an audit intern and obtaining a full-time offer works towards Deloitte's mission. Deloitte only wants to hire the best of the best who fit with their culture and values. Once you join Deloitte, how you conduct yourself and your work performed reflects on the Company.
Deloitte treats interns as if they are first year associate audit employees. This may sound daunting, but they prepare you very well. An intern is just as valuable as a full-time employee, and everyone regards interns as such. They are given real work to do, not coffee runs or busy work. Interns truly contribute to the end products which the teams are working on.
I think Deloitte's mission is very client oriented and with audit you're on the client site every day and working with the client frequently (not always directly as an intern but you see it every day in the office). However, Deloitte has many missions and providing client value is just one of them. In audit, it's interesting because you are hired and work for the client company, but the work you do and its quality affects investors and the market in a broader sense. Being an external audit intern you get to see how your work goes into satisfying two pretty lofty goals at once.