Answer by Gil Yehuda:
I’ll add a little color to the excellent answers here which could explain the strange but understandable relationship between how copyright law is designed to work, and how it applies to open source code. Moreover, I’ll explain why we are in the situation we are in with code, copyrights, and open source licenses
Imagine you were a freelance writer working in Hollywood who wrote movie scripts. You spent hours writing what you thought was a fantastic movie with great dialogue. You pitched it to a movie executive who rejected the story, crushing your dreams of stardom. Somehow, someone got hold of your movie script and thought it was quite good, so she pitched it to a different producer, and landed a great deal for her, using your script (maybe she modified it, or not). You’d probably be upset.
Copyright law protects your creative works (not ideas in your head, but the script you record on paper, a picture you take on film, a story you record on tape — or code you write on your computer), so that only you have the right to copy that work (right to copy = copyright). Someone else who finds your work cannot make a copy of it without your permission, nor can she display or perform your work without your permission. And she can’t present it to her favorite movie executive — even if she admits that she did not write the script; even if she says you wrote it. It’s not hers to share, it’s yours. The copyright protects you from someone taking your stuff without your permission. Of course, since you have the right to your movie script you also have the right to allow this other person to pitch it to a different movie executive — but she’d need permission from you — a license. You might pay her to pitch the script for you, you might ask her for money to have the rights to pitch the script. Or you might just share the script with her as a collaborator. You get to decide.
When developers started to write source code in the 70’s, lawmakers felt that source code was similar to movie scripts. They involve creative effort and people are willing pay, therefore they should be given the protection that other works of literature would get. Eventually, the Open Source movement began to inspire many developers to think about their code differently; that sharing their code permissively with other developers was worth more than keeping the code under copyright protection. Open Source projects demonstrated that opening code has significant value to the code quality, to the original author, and to the community of developers. Now, many developers would rather open their code so that others could use it and add to it. But the copyright-by-default laws creates the situation that if another developer takes your code (even if you were OK with it conceptually), you could decide to sue that developer (much like in the movie script case). Open Source licenses were created to enable authors to give explicit permission to others developers to use the code — protecting the intent of sharing from unintended legal consequences.
As others have said in response to this question, the copyright is a statement that expresses the legal fact that you (or your company) owns the copyright on the code. You have a right to copy the code, and you have the right to grant others the right to use the code. The license is an expression of the right you grant others to use that code. You cannot grant rights to use code if you don’t have the rights in the first place. So you need the copyright (and it’s very helpful to add it explicitly), and then you can add the license on the code. If you just have code with no license, other people do not have the right to use the code (even if you don’t mind, you need to be explicit so that they know you are giving them permission). Open Source licenses grant broad permissions with (usually) very few conditions of use. Most common is that you have to give credit to the original author. Under some licenses, you have to be explicit about the changes you made to the code so that others can tell what you added. Other licenses require that changes you make to the code be publicized under certain conditions. So the specific open source license you use does matter.
Back to being the movie script writer: lets say you wanted to write a script and publish it so that anyone could use it, could modify it, and could perform it (in other words, you’d rather build your reputation by giving your script for free, and getting feedback on it, instead of the all or nothing pitch to a movie executive). You could “open source” the script, but you would not use an Open Source license, rather an Open Content license (like the Creative Commons licenses which are designed for content). You’d still have the copyright on the script, and then you’d add the permissive license telling people they could use it (under the specific terms you select based on the license type you choose).
Note: I am not a lawyer. Corrections to the above are invited.