Economics and the Public Interest
The primary story of copyright in U.S. law focuses economic incentives and social progress. The U.S. Constitution gives Congress the ability "...to promote the Progress of Science and useful Arts, by securing for a limited Time to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." All of U.S. copyright law (and patent law) grows from this one brief phrase in the Constitution.
If you create a physical object, you can use physical means to control who gets to use it. But creative and expressive works are a little harder to control: if you write a book and want to control who gets to read it, the minute you let a copy out of your hands, you've lost a lot of control. The person you gave the copy to can pass it on to someone else, make a new copy, or even memorize pieces of it and recite them in public! Copyright deals with these problems by providing laws to control ownership and distribution of creative and expressive works.
The purpose of copyright, then, is to create mechanisms to control ownership and distribution of expressive works.
Secured to Authors
If copyright didn't exist, everyone would be able to make copies of each new creative work without the creator's permission. But because it does, creators get to decide whether or not their creative works get distributed, and how they get distributed. And if lots of people want copies of the work, the creator can make people pay to own those copies.
The purpose of copyright, then, is to create mechanisms for creators to control ownership of expressive works, so they can receive payment for their works.
Most creators, this story goes, create their works because they know they are able to get paid for the copies people want. Because copyright enables creators to get paid, more creators make more works. And more creative and expressive works is good for society, because it helps us develop arts, science, knowledge, and culture.
The purpose of copyright, then, is to create mechanisms that help creators control and receive payment for their works, because that will result in the creation of many more expressive works, which benefits all of society.
"Moral Rights" for Creators
Many countries have copyright systems based on "moral rights" justifications, rather than the incentive theory that's popular in the U.S. and other common law countries.
"Moral rights" are thought to arise naturally out of the deep connection that creators have with their works. Because of that connection, this story goes, the law must recognize creators' rights around attribution and reputation. In copyright based on moral rights theories, creators have some economic rights (such as the right to make copies), but they also have parallel rights to attribution and to prevent uses of their works of which they disapprove. In many countries, the moral rights cannot be sold or given away, and remain with the creator no matter who controls the economic rights.
...on Copyright Theory, Generally:
Introduction - Copyright for Librarians, Berkman Center for Internet & Society
...on Economics and the Public Interest:
Collected research documents from the Society for Economic Research on Copyright Issues
...on Moral Rights:
Moral rights (copyright law), Wikipedia
Moral Rights Basics, by Betsy Rosenblatt, Harvard Law School.
Copyright's Purpose: What Copyright is For | Functional © Fundamentals | The Public Domain | Exceptions & Limitations: Classroom Use, Fair Use, and more