Free as in free beer
Socially I have led various usergroups in my community for techs and devs, and at some of them we've offered beer, sodas, and pizza. There was no requirement, no purchase, just a friendly offer for you to come and have some beer that I provided. It was my beer, but I was welcome to share it with whoever came along (most software repositories that you use are "free beer" in that there is no encumbrance with the software, you just have to show up to get it).
We would possibly also use the words gratis or gift or maybe the phrase at no price (and sometimes at no cost when a company releases it) to describe this "free" (but note that the legalities of calling such a thing a gift in most English businesses would cause problems, so don't refer to it that way, just understand it that way).
All you were given was the beer, and it was not given with the intent of making you listen to a sales-pitch (sometimes people do this, which is also an occasion for free beer) or of making you contribute back. It was an enticement.
As others have pointed out, I in no way gave others the liberty or capacity to resell the beers, to brew their own with a recipe (I didn't even have the recipe) or any other such "allowance". But so long as you showed up and socialized, the beer was free for the asking.
This is "free as in free beer".
Free as in free speech
In the US we have our nearly world-renowned "First Amendment" which simply states:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
So how is software also like free speech?
There is no way in this day and age for someone to stop you from writing software if you want to, so long as you can achieve the capacity of a computer to run an O/S on. Because of the "free beer" Linux and the related distros, you're able to run an operating system that affords you all the capacity to write software. A computer can now be had for less than $300 in the US, and similar amounts in the rest of the world, so they are not considered overly priced.
Because you have the tools (a lot from "free beer"), no one can restrict your right as a reasoning human being from writing software. There may be limitations on how you distribute it, or how it's used (you can write viruses all day long, but using them may land you in jail. The counterpoint is you may protest in a public place, but the police may arrest you for obstruction if you have created a harmful situation), but there is no limitation on how you may create software.
It is as much your right as is your right to free speech.
In other places we might call this liberty or freedom or not restricted.
But just as it is highly unwise to brandish a rifle and scream that you want to kill the leader of your country (which is not considered free speech), there are some moral restrictions to software authorship that the community or the law may not be happy with. So when I say "not restricted" please bear this in mind.
