We've all met annoying, egotistical people who love to brag about themselves. Most college students seem to be particularly sensitive to this and would never brag to their peers. However, they carry this same attitude into the interview. Students frequently tell me that they are hesitant to brag about themselves in the interview for fear of being viewed as arrogant or egotistical. Sometimes this is a reflection of having been brought up in a different culture than the U.S. but I also see it in students who were born here. I always tell them that, while humility is a virtue, the interview is not a place to be humble. Bragging to your friends about your accomplishments is, well, bragging. But bragging in an interview is "selling yourself" in order to get the internship or job.
When you go on an interview, the objective is to present yourself in the best possible light to the employer so that they will want to hire you. So you need to feel confident about talking about yourself, highlighting your strengths and skills that would be relevant for the position and expressing your significant accomplishments. Believe me, the interviewer will not perceive this as bragging! Interviewers want to hire confident people, so they will be quite impressed that you are a person who can speak confidently about yourself! They are also investing a lot of time and money in the hiring process and need to make sure they are getting an optimal return on investment by hiring the best candidate. And how would they know you're the best candidate unless you tell them!
If you're still feeling reluctant about selling yourself during the interview, conduct mock interviews with counselors at your career center who will be able to coach you on how to present your key skills, strengths and accomplishments in a confident, polished manner. And, if you're concerned at all about coming across as arrogant, no need to worry! Chances are that you are far from being arrogant, but if you are, your counselor will let you know it.