A copyright owner has the right to control a lot of uses of their works, like making copies (of all or part of a work), distributing copies, showing or performing a work in public, and making new works based on existing ones.
We all make many uses of creative works. Some are more passive - reading, watching, listening; and some are more active - citing, copying, remixing. Many very simple, everyday uses, like forwarding an email (you just made a copy!), or watching movies with friends (is that a public performance?) overlap with, or "implicate" copyright rights.
In fact, there is a lot of overlap between uses people make of copyrightable works, and the kinds of uses copyright owners control.
It's really important to remember there are many limitations and exceptions to copyright owners' rights, and many types of uses that are exempted in certain circumstances. So even though the uses people want to make overlap a lot with the uses owners control, there are many situations where the use is allowed!
Sometimes you may be able to use something because it falls under an exception or exemption to copyright law - for example, small business owners may be able to play music off the radio (which would otherwise be a public performance, requiring permission) because there is a specific exception in the law for small business use of broadcast media! Other times, you may be able to use something because your use fits within fair use, a flexible-but-confusing part of the law that enables many different types of uses under many different conditions.
Using Copyrightable Materials:
Making a Use Decision | Fair Use | Thinking Through Fair Use | Guidelines and Best Practices | Getting Permission
Use in Context:
Teaching Uses | Research and Writing Uses | Multimedia Use | Student Use