Your letter of assignment is a letter provided by the editor/publisher who is paying you to take the photos.
In other words, are you going to take photos for your local paper, a magazine, a website, etc? Whoever you are taking the images for, is who needs to provide a letter stating your assignment for them.
If you aren't shooting an assignment and are shooting on spec or for yourself, you can request credentials, but depending on the event/volume you'll probably be denied. Credentials are typically handed out to members of the press or freelancers who are shooting on assignment for a publisher or source.