Professionalism, in general, refers to how people behave while on the job--many aspects of professionalism are also known as soft skills. 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 employee as your actual job/task performance.
Here is a list of the most important components of professionalism, as suggested by faculty, internship site supervisors, and former interns:
1. Punctuality and Dependability
When an employee is hired, hours and days of attendance are generally agreed upon at the beginning and the employee is expected to be at the site (or in contact, for a remote position) for those days and number of hours unless there is a legitimate reason (e.g. illness, family emergency) that causes the employee to miss work. If such a situation arises, the employee should follow whatever procedure is in place for reporting missing work--usually at minimum contacting their direct supervisor.
When an employee does not report to work 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 not only the employee's supervisor but also his/her co-workers.
Bottom line: whatever schedule you negotiated, adhere to it--very few jobs allow employees to make their own hours and/or come and go as they please. If the hours/days aren't working for you, talk to your 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 employee (especially as a new employee), 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 supervisor what the expectations are for your site/office, 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 and/or need to wear a uniform). 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
What to Wear: "Professional" vs. "Business Casual" from Princeton University Career Services
Professional Attire Basics: Understanding Dress Expectations for the Interview and at Work from University of Denver Career Services