A few disclaimers here:
Internships are, by and large, associated with the college experience here. I went to school for journalism, and my internship was with the Denver Broncos, a professional American football team, producing content for their website, game day program, and the NFL network. It wasn't a UX internship by any stretch of the imagination.
I never finished my degree, and I never went back to school for UX. Therefor, my experience with internships in the UX & technical world is pretty limited.
That said, internships over here are seen as a necessary part of the college experience. Pretty much everybody will do one, and in general the larger the organization the better the prestige associated with the internship. What you do in an internship varies a lot. At some companies, you will have a very hands-on roll, while at others you may become nothing but an errand boy/girl. Either way, it's all part of paying your dues, so to speak.
I think your focus on learning, accepting that making mistakes is part of the process, and making good connections within the industry is where you mind should be. You'll do great, @caglar_araz! I can't wait to hear about the internship and what you get up to. Keep us up to date, will you?