Interns are the lowest of the low. Everybody's time is more valuable than yours right now. Therefore, only take other people's time if it's work-related, not too much time, and worth both your and their time. Anything else is likely to annoy people. Nonetheless, interns are supposed to learn, so if you can quickly explain your goals and keep it brief, it shouldn't be too bad.
Ask about how a co-worker or supervisor does their job.
Do you have a work-related reason to need to know this? If not, then how much time would be required for them to answer? Is the importance of the question worth both your and their time?
Ask away if you think that the answer is yes, not too much, and yes, but hold your tongue otherwise. Since you're an intern, the default answer is no, too much, and no, unless the person is a designated mentor or something.
If you are genuinely curious about these details, then consider asking them at a work-related but more relaxed venue, like in a break room, or at a company party (assuming people are comfortable talking about work when at those places.) Either way, keep it brief.
Finally, be sure you don't sound like you're looking to criticize. Lots of people think they know everything about everything everyone else does. The last thing you want is for people to think you're one of those people, but it's all-too-easy for that to happen when you're new and asking lots of questions.
Give lengthy answers to questions coming from people. Like explain why I did my work in a certain way.
The same exact questions can work here. Do they have a work-related reason to know everything you're telling them? If not, then how much time would be required for them to listen? Is the importance of the question worth both your and their time? Once again, as an intern, the default on these is no, too much, and no. Answer as concisely as you can without losing important details, unless they really want to know details, in which case, go right ahead.
My interest was in knowing how my role fits in the bigger picture so i can better serve them
Do they know this? This is the kind of thing that might help them see how this is work-related, won't take too long, and worth the time to answer. It would be great to preface your questions with something like this (the first time.)
Be careful with how you phrase even this, since it could be taken as criticism of your supervisor, since you clearly feel like they're not giving you enough direction. This mostly applies if you're talking to your supervisor's direct superior, although I don't see why you would (as an intern) do that.
Finally, don't worry too much
You're an intern. A certain level of annoyance is expected. I'm sure you'll figure things out soon enough, and even if you don't, you'll just be better prepared for later.