A copyright is a form of protection provided by the laws of the United States to authors of "original works of authorship." This includes literary, dramatic, musical, artistic and certain other creative works. Material not protected by copyright (or otherwise protected) is available for use by anyone without the author's consent. A copyright holder can prevent others from copying, performing or otherwise using the work without his or her consent.
Generally speaking holding copyright to a work is the legal right to be the only one to reproduce, publish, and sell a book, musical recording, etc., for a certain period of time. So, the mere act of making a copy of a copyrighted work - even for your own use - is a violation of copyright. For printed material this is relatively easy to understand. But, in this era of easy access to digital media (video, audio, pictures etc.) adhering to copyright can become murky.
Fair use is a legal doctrine that portions of copyrighted materials may be used without permission of the copyright owner provided the use is fair and reasonable, does not substantially impair the value of the materials, and does not curtail the profits reasonably expected by the owner. Specifically in educational fair use it means that for example a video can be shown in class as long as it is used to support the teaching of the class. But this fair use does not extend to making unauthorized copies of the video or putting them on a server for campus-wide access.
Thus, fair use can have many gray areas that should be carefully considered before assuming fair use.
The "copyright" and "fair use" tabs in this guide will give you links to sites that can give you guidelines and more detailed explanation of these legal doctrines.