First, the sole purpose of a cover letter is to get someone to look at your resume. That's it. It isn't to tell your life story or even get you an interview. It's just to get them to click on the link to your resume and invest some of their time to take a look and consider you. Again, it's really that simple.
So, your cover letter should answer these questions, from the point of the view of the person reading it:
- Why are you contacting me?
- How did you find me / this job or internship?
- Why do you want this job or internship?
- Why are you a good candidate for this job or internship?
- What about you makes me want to know more?
Admittedly, answering those questions in one succinct letter or email is easier said than done. Still,, the point is that you don't need to explain everything you've ever accomplished or try desperately to convince them to hire you on the spot. You just need to pick a few key examples, explain yourself, and leave them wanting more.