The letter is important because it is the first impression that the recipient of the application gets of you.
It should state who you are and what you do, that you are interested in an internship position, and why you find this particular laboratory interesting. To make the latter point, it is enough to mention that you are interested in the respective field (e.g. cell cycle regulation or prions), mention an article by that particular person, and say that this is a topic that you would be interested in working on. (This does not actually commit you to working on that subject later, just that this is something that you could imagine doing. It is no use detailing an exact project since that is determined by the head of the laboratory anyway.)
Close on the note that you feel that your training so far enables you to make a small contribution to a research effort, and that you are highly motivated to do so. The letter should be 1.5 pages maximum. If you would like further inspiration, I have put together a sample letter with comments.
Even in these days of e-mail, it is advisable to send a letter on paper. The first impression that you make is very important, and you have no control whatsoever over the formatting that the recipient's e-mail software will give your letter. Also, professors usually receive several e-mails per day soliciting internships which are usually mass mailings. Thus, most are suspicious towards e-mails. The most promising way to success, in contrast, is to stand out by quality.
If you have a non-Western name take care to write your name in the correct manner: either "Firstname Lastname" (e.g. Fred Miller) or "Lastname, Firstname" (e.g. Miller, Fred). Otherwise there will be a confusion about what your name is, and your file may get lost.
The best way to writing an excellent letter is to use (but not to copy slavishly) letters of senior students, to have your letter proof-read by the service that exists at IUB for this purpose, and to have faculty look it over before you send it.
Potential internship hosts want to know about your personal history, the initiative with which you have followed your interests (in- and outside science) so far, and the depth and quality of your theoretical and practical training. Your CV should tell about these things. Especially, it should have a brief description of the contents of courses and your practical laboratory experience. Further information on writing a scientific CV is here.
The best way to writing an excellent CV is to use (but not to copy slavishly) those of senior students, and to have faculty look it over before you send it.