No law says you have to submit a cover letter along with your Form N-400 application for naturalized U.S. citizenship – but doing so is a good idea. It allows you to summarize what you are submitting to U.S. Citizenship and Immigration Services (USCIS) and to alert the agency to any special aspects of your application.
If, for example, you will be reqesting a waiver of the English language or civics exam requirement due to your age, the cover letter is a good place to highlight this. Or, if you have a disability that requires special accommodations, the cover letter will help bring this to USCIS's attention. (Both issues are covered within the N-400 itself, but it never hurts to remind USCIS of important features in your case, so that the officer is prepared.)
Another advantage to preparing a cover letter is that it allows you to read it through one last time and make sure everything is included before you send your packet to USCIS!
(See Nolo's articles on “Application Process for Naturalized Citizenship” for more on this process.)
If you find that this process is difficult to handle alone, get more advice from an experienced immigration attorney.