Free in Free Software is referring to freedom, not price. Having been used in this meaning since the 80s, the first documented complete definition appears to be the GNU's Bulletin, vol. 1 no. 1, published February 1986. In particular, four freedoms define Free Software:
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.
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.
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.
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.
These freedoms are rights, not obligations, although respecting these freedoms for society may at times oblige the individual. Any person can choose to not make use of them, but may also choose to make use of all of them. In particular, it should be understood that Free Software does not exclude commercial use. If a program fails to allow commercial use and commercial distribution, it is not Free Software. Indeed a growing number of companies base their business model completely or at least partially on Free Software, including some of the largest proprietary software vendors. Free Software makes it legal to provide help and assistance, it does not make it mandatory.
Free Software is the original term for software that respects freedom, and there are important reasons why this terminology continues to be used today. Free Software connotes freedom, and when translated there is a clear distinction between freedom and price. In French, Free Software becomes "logiciels libre", "software libre" in Spanish, "software libero" in Italian, and "Fri Software" in Danish.
On February 3rd 1998, in the wake of Netscapes announcement to release their browser as Free Software, a group of people met in Palo Alto in the Silicon Valley and proposed to start a marketing campaign for Free Software using the term ``Open Source.'' The goal was to seek fast commercialisation of Free Software and acceptance of Free Software by the companies and venture capitalists of the booming new economy. As a means to this end, they made a conscious decision to leave aside all long-term issues (such as philosophy, ethics and social effects) related to Free Software, feeling these posed obstacles in the way of rapid acceptance by economy. They proposed to focus on technical advantages only1.
Often used in good faith by people who refer to what Free Software stands for, the term "Open Source" - originally defined to mean the same thing as Free Software in terms of licenses and implementation - has seen inflationary usage. Nowadays, it is regularly used for everything between Free Software and the highly proprietary "Governmental Security Program" (GSP) by Microsoft2.
When the European Commission started dealing with Free Software on a regular basis, they sought to avoid the ambiguity of the English word "Free Software" and the misunderstandings of "Open Source" alike, which led to the adoption of a third term which has popped up occasionally since around 1992: "Libre Software." This term has proven resistant to inflationary usage and is still used in an identical way to Free Software. So it may pose a solution for those who fear being misunderstood when speaking English.