For instance, in a typical job application, the problem is that the company or organization needs a position filled, and more importantly they need someone who can do the job well and help the organization achieve its mission (which may be more profits, or it may be to save children in Darfur or to end global warming or to cure cancer). You arouse their interest by telling them that you’re the right person for the position and by promising to help them achieve their mission.
In these days of email and instant messaging, letter writing is becoming a lost art, and especially the formal letter. I’m pretty sure that formal letter rules are still taught in schools, but very little of it sticks. If you’re an executive or other high_ranking person within an organization, you can probably rely on your secretary or assistant to handle the niceties of letter writing, but for everyone else, knowing how to write a strong letter ourselves is important.