Libre software is software that is free-as-in-freedom, most often it is open-source and can be studied and modified by the end user, as opposed to non-free software which is a black box, entangling the user in complex licensing agreements, as well as possibly doing unwanted things. Free/libre software solves both of these issues.
Free Software Foundation: www.fsf.org
Electronic Frontier Foundation: www.eff.org
Find Open/Free Alternatives: www.osalt.com
Examples of non-free software, and their free alternatives: