An intern is usually someone who is stuyding at college and needs "work experience" for college credit. It's not a real job. It's an arrangement with the company to allow a student to learn more about their chosen feild, right in the workplace. It's usually unpaid, part time (a few hours a week) and temporary (two or three months).
In Europe, it's a bit different ... usually called "work experience", it's often paid and they are not regulated by laws that say you must be getting college credits for it. So,. sometimes people are able to get work experience without being in college.
The purpose of an internship is to learn about how the business works from the inside. You observe while you work. Internships are not just in fashion ... they are offered in almost any type of business ... the porocess and goal is the same.
The work you would do is usually what we call "grunt work". In the case of working at a designer's atelieir or a fashion magazine it might include taking care of the sample clothes, ironing,loading and carrying clothing on racks, delivering things for the company, getting coffee for everyone, answering phones, computer input, photocopying or anything else they need someone to do, which does not require any training.