The internship letter is what you write in the email that you send to prospective employers along with your resume. The internship letter is not the same as your resume and should, therefore, contain details apart from what your resume mentions.
The focal point of the internship letter remains the reason as to why you want to pursue an internship with that company. This could also be seen as a statement of purpose. As there are chances of you being judged by the internship letter there should be no scope for any error in the internship letter. Your purpose should be clearly stated in the letter. The sentences should not be unnecessarily lengthy. The point that you are trying to convey gets lost somewhere in the length of the sentence. The sentences should also be grammatically correct. If you do not have a good grammar, please ask someone to help you out with that. The person who reads your letter might be very particular about the grammar. It also does not reflect well on you if your letter has errors.
Also mention why you think you would be suited for the job over so many other applicants who must have applied. You do not need to resort to hyperbole. The people will see through it and you might stand the chance of being rejected. Just give an honest answer as to why you would be suited for the job.
You could also include past experiences and accomplishments in your letter. But, try writing down that stuff which would enhance your candidature. The resume can include the details of other accomplishments, not the internship letter.