Professionalism, in general, refers to how people behave while on the job--many aspects of professionalism are also known as soft skills. Even as an intern--some employment experts would say especially as any intern--how you conduct yourself in general and how you present yourself to clients/customers, coworkers, and supervisors is just as important to being a successful intern/employee as your actual job/task performance.
Here is a list of the most important components of professionalism, as suggested by faculty, site supervisors, and former interns:
1. Punctuality and Dependability
When a site accepts a student as an intern, the expectation is that the intern treats their internship like any paid job--hours and days of attendance are agreed upon at the beginning and the intern is expected to be at the site for those days and number of hours unless there is a legitimate reason (e.g. illness, family emergency) that causes the intern to miss work. If such a situation arises, the intern should follow whatever procedure is in place for reporting missing work--at minimum contacting their site supervisor and the Central Penn Internship Coordinator.
While being at your job when you are expected there is always important, for an internship it is even more necessary because an internship is a supervised work experience. In many cases, the site supervisor modifies their schedule to work with and supervise the intern, so unless an intern has negotiated for a flexible schedule--when an intern does not report to the site as expected, and/or does not report at the consistent days/times agreed upon, that is not only unprofessional but might also be considered disrespectful of the site supervisor and his/her time.
Bottom line: whatever schedule you negotiated with your site supervisor, adhere to it--very few internships (or jobs) allow interns to make their own hours and/or come and go as they please at the internship site. If the hours/days aren't working for you, talk to your site supervisor to see if then can be modified.
Attitude as it relates to professionalism refers mainly to how you come across in your dealings with people, how do other people perceive how you act. An appropriate attitude for most workplaces is one of confidence without cockiness, politeness with friendliness, and being helpful without being completely submissive. Your attitude with coworkers and supervisors is almost as important as your attitude with customers/clients. In most workplaces, multiple people with varying personalities need to work together to accomplish the company or organization's goals, and having a professional attitude is an important part of being easy to work with and able to contribute to a group.
As an intern, it is important to be aware of what you do not know, what your limitations are, and to be careful to not make assumptions that could cause you to appear arrogant. However, you should demonstrate assertiveness and willingness to try tasks/software/technology you have not used/done before.
Dress expectations for business have relaxed significantly in the last few decades--it is no longer standard for men to wear suits and ties and for women to wear suits/skirts/dresses and heels. However, many businesses do have some sort of dress code or expectations of their employees. Be sure to discuss with your site supervisor what the expectations are for your internship site, and pay attention to what the other employees are wearing. If you are in a customer/client-facing position, be sure to confirm if there are higher dress expectations for meetings, etc. than for regular office times.
Dressing slightly better than the dress code requires is a good idea for most jobs (unless you're working in an environment where you'd get dirty). Even if you are lucky and the office dress code allows you to wear jeans and sneakers, you should still dress neatly wearing jeans without rips/holes and sneakers that aren't dirty.
Here are several good web articles about the various levels of 'dress code.'
How to dress your best in any work environment, from a casual office to the boardroom from Business Insider
Business Professional Attire vs. Business Casual Attire from The Balance: Careers
Professional Attire Basics: Understanding Dress Expectations for the Interview and at Work from University of Denver Career Services