"Libre software" means software that respects users' freedom and community. Roughly, it means that the users have the freedom to run, copy, distribute, study, change and improve the software.
In particular, four freedoms define Free Software:
The freedom to run the program, for any purpose.
Placing restrictions on the use of Free Software, such as time ("30 days trial period", "license expires January 1st, 2004") purpose ("permission granted for research and non-commercial use", "may not be used for benchmarking") or geographic area ("must not be used in country X") makes a program non-free.
The freedom to study how the program works, and adapt it to your needs.
Placing legal or practical restrictions on the comprehension or modification of a program, such as mandatory purchase of special licenses, signing of a Non-Disclosure-Agreement (NDA) or - for programming languages that have multiple forms or representation - making the preferred human way of comprehending and editing a program ("source code") inaccessible also makes it proprietary (non-free). Without the freedom to modify a program, people will remain at the mercy of a single vendor.
The freedom to redistribute copies so you can help your neighbor.
Software can be copied/distributed at virtually no cost. If you are not allowed to give a program to a person in need, that makes a program non-free. This can be done for a charge, if you so choose.
The freedom to improve the program, and release your improvements to the public, so that the whole community benefits.
Not everyone is an equally good programmer in all fields. Some people don't know how to program at all. This freedom allows those who do not have the time or skills to solve a problem to indirectly access the freedom to modify. This can be done for a charge.