Well, basically, copyright is a part of federal law that guarantees that when you create a piece of intellectual property*, that you can control how it's distributed, recreated, and how revenue is generated from it.
Why is this important, you might ask? Well, copyright protection incentivizes innovation; it encourages creators to develop new works, because they know those works will be protected. Think about it; without copyright protection, would The Lord of the Rings movie trilogy ever have been made? Would any studio have invested that many millions of dollars into making those films?
* "Intellectual property" refers to anything material that you create: papers you write, songs you record, sculptures you execute, photographs you take, movies you film, software code you compile, etc.
"So what does it mean to 'infringe' copyright?"
Well, anytime you take for yourself, without permission, any of the rights that a creator is specifically and exclusively granted under 17 USC § 106, you're infringing copyright. In terms of piracy, here's a quick, loose rule of thumb to help you tell whether or not you're infringing:
If...
-you are not the creator of the work, AND
-you have not paid to own a copy of the work or acquired permission to own a copy, AND
-the work is a commercial product that you normally would have to pay for...
...then copying the work or redistributing it is probably an act of infringement.