A cover letter is a short business letter that accompanies your resume and serves as an introduction to it. It's a chance to customize your particular qualifications and experience for a specific job opening or prospective employer.
Why write a cover letter for your resume?
A well-written cover letter allows you to attract the reader's interest. Don't expect a cover letter to do all of the work, though. It's best used when it fits into an overall marketing plan—and every good letter needs a "hook" to engage the reader.
The "hook" is always best baited with something of interest to the reader: for example, a business manager will be more interested in a letter that appeals to his or her need for efficiency, productivity, and most of all, profit.
The hook for an institutional decision-maker is more likely to require some research. What's the institution there to do? What is its mission? How can your skills and abilities support that mission?
One thing that will keep the reader hooked once you have their interest is if you can "borrow" someone's trust. Everyone has to trust someone (even Mulder on the X-Files): friends, family members, colleagues. For that reason, if you can "drop a name" in the cover letter, and that name belongs to someone the reader trusts, you'll have the benefit of that trusted person's goodwill. This name dropping is called "implied referral." (There are several examples of implied referral in the cover letter, linked from the bottom of this page. See if you can find them.)
Now that you've hooked your reader, and have kept their interest, it's time to try to land the big fish (get an interview!) It's important your cover letter lead somewhere: it should end with a request for an interview, or a promise to follow up with a call about an interview. Don't be afraid to ask for an interview; that shows the reader you're interested in doing business. The reason for every cover letter, resume, and application is to get the interview, and what you want the cover letter to do is get your foot in the door. Or, to continue our fishing metaphor, to get your feet wet.