All professors are not the same, therefore their selection criteria may differ. However, there are certain key criteria that most professors look for when selecting candidates.
Interest for the subject matter. You need to establish that you have a desire to work on the project you are studying. If you have an interview, it can show if you talk about recent articles published from the lab, articles in the field, and some ideas aims you hope to accomplish in the project. If you don’t have an interview, then you need to establish early on in your email communications to the professor that you have looked at several papers already on the topic. You should always ask for references to other papers the professor thinks would be of interest to you.
Good grades. Good grades say a lot. If a professor receives multiple applications for a single undergraduate research position, then often or not, the filter will be the undergrad GPA. However, I have often seen students with stellar GPA, but lack a good work ethic in the laboratory, interacted poorly with other lab members, or have an inability to just do the physical work despite having a great ability to plan an experiment.
Recommendations. The power of the recommendation is understated. Recommendations are critical when applying for extremely research competitive positions. The recommendation can come from a course you took, from another undergrad in the lab you want to join, or from a graduate or postdoc which you have gotten to know prior to applying for a research position. Recommendations go beyond your list of accomplishments. They reveal into your personal skills