Hi Brandon, great question! There are several things I paid attention to while applying for an internship. The first was my resume. I made sure that I not only tailored my resume to the specific application, but I also thoroughly reviewed my resume. Believe it or not, many applicants forget to double check their resumes for errors. If you are in doubt about the quality of your resume, i'll suggest getting it checked by your school's career center or a professional. Organizations and extra curricular activities also look good on your resume. This is because it shows that you can handle multiple responsibilities. Also, I would advise you to use many facts and figures in your resume.
Another way to stand out in your application is through your cover letter. Make sure you tailor your cover letter to the internship you are applying for. If you are unsure about how to tailor your cover letter, look at the internship posting and read the description. Most companies give specific details about the skills and experience required for the internship. I hope this helps. Good luck on your search!