Apple has a culture of extreme attention to detail. No detail is too trivial. So even as an intern you need to be thorough with your work.
You won’t be micro-managed so make sure you manage your time well and regularly seek feedback from your manager and mentors about how you’re doing.
Keep meeting new people and talk to them about the work they do. You won’t get project details because secrecy is taken seriously but you can always talk about what their role is about. People are generally very nice to interns so it’s totally okay to ask anything and everything you want to know.
Find your work-life balance. Enthusiasm and the general inspired atmosphere in the company will often drive you to put in long hours and maybe even work weekends. But it’s essential to give yourself a break every week to prevent burnout.
At Apple, you have to be heard. Apple is not a "run of the mill" tech retailer, they want you to ask questions and provide input. You don't want to put your head down and work here. If you want change, you have to be the change and lead others by example.