What is Free Software?[]
The phrase "free software" in a computer science and programming sense, refers to a style of software that is relatively unencumbered by commercial interests, both with respect to monetary policy, and intellectual freedom to modify and explore how a program works by digging through its source code.
Defining Free Software[]
A more accurate term for free software as defined above would be FLOSS, or Free Libre Open Source Software, which is a term that acknowledges both a lack of cost, and the freedom to do what you will with the software. When referring to applications that are distributed as binaries, without cost, a more accurate term for this is Freeware. Freeware generally does not come with source code, and does not use a free software license recognized by the Free Software Foundation.
Not "Public Domain"[]
Please don't confuse Open Source software as public domain! In most countries where copyright is respected, a FLOSS program is still attributable to the people that wrote it, and furthermore is often governed by a software license like the GPL. These licenses come with requirements that define what you may or may not do with the software. See the GPL article for an example of the freedoms offered under this very popular FLOSS license.