When I was in college, my department required each student to complete two internships to graduate with our major's degree. There were prerequisite courses that had to be taken before each internship. And to top it off, one of the internships had to be completed during a semester (so you couldn't do two summer internships).
At the time, it seemed like a huge inconvenience to have to complete these internships, specifically the one during the semester. It would delay my graduation and therefore cost extra money in tuition and room and board fees. Yet, once it was time for me to apply to full-time jobs, I realized that the internships I completed were actually a boon to my job search.
1. Internships provide real-world experience.
It can be difficult for a student to imagine how things work in the "real world" when all they've done their entire lives is study. The experience that an internship can provide is invaluable and can get you ahead of your competition. Employers will see the practical experience on your resume and know that you understand the basics of working in your field.
2. Internships connect you with professional references.
If you perform well during your internship, you can (and should) ask your supervisor to be a reference. Your candidacy will be stronger if you have references in your field instead of summer job supervisors or professors.
3. Internships (sometimes) let you earn money.
Not all internships are paid. One of my internships had a stipend of $150 per week, which isn't much if you are not living rent-free. I had another, part-time job to supplement the money I made at the internship. It was a lot of work for 12 weeks, but the experience I gained from the internship was worth it.
4. Internships show a dedication to your future.
Simply finding, applying for, and accepting an internship shows initiative. While some students are milking their "free time" as much as possible, you can begin to lay the groundwork for your professional career. It doesn't have to mean all work and no play; a full-time internship still has evenings and weekends free so that you can enjoy yourself!