Free software

Free software allows the user to legally use, study, modify and redistribute the source code of a program. The term "free software" does not refer to price. Free software may be obtained for a fee, though it will likely be low, or free of charge - especially when downloaded from the Internet. According to the definition given by the Free Software Foundation, a program, to be considered Free Software, must offer "four freedoms" to its users:

The freedom to run the program, for any purpose (freedom 0).
The freedom to study how the program works, and adapt it to your needs (freedom 1).
Access to the source code is a precondition for this.
The freedom to redistribute copies so you can help your neighbor (freedom 2).
The freedom to improve the program, and release your improvements to the public,
so that the whole community benefits (freedom 3). Access to the source code is a
precondition for this.

Licenses

Most free software is licensed under the GNU GPL (General Public License), a license created by the Free Software Foundation for its GNU operative system. Other licenses include the BSD (Berkeley Software Distribution) license, used by the aforementioned software package created by the Berkeley University, and the GNU LGPL (or Lesser General Public License) by the Free Software Foundation. These licenses diverge mainly by their permissiveness: while the GPL only allows the programs licensed with it to be combined with software using the same license (or licenses that don't conflict with it), the BSD license can be used without restriction, even in programs that aren't free software. The LGPL, on the other hand, is an intermediate step, that allows any other programs to use the code, but require modifications to the code originally licensed under the LGPL to be kept under the same license.

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References

Free software definition
The GNU General Public License