Closed software, proprietary software: You buy a loaf of bread from a business. You’re not allowed to figure out the recipe, you’re not allowed to share it with friends and family, and the bakery has the right to take it away from you if they don’t like the way you’re eating it. Examples: Windows, MacOS, Adobe’s various software.

Freeware: You get a free loaf of bread from a business. You’re still not allowed to figure out the recipe or to eat it in a way that the bakery doesn’t like. Depending on the license you might be able to share that bread with friends and family, but it might instead limit you to telling them where they can get their own free loaf of bread. Examples: First-party apps on phones, such as Google’s own Android apps or Apple’s own IOS apps.

Free software: You get the loaf of bread and the recipe for free. You can share either as much as you want with anyone. You’re free to tweak the recipe and share the tweaked recipe with others. The only thing you can’t do is distribute bread made with your tweaked recipe without also providing that tweaked recipe for free. Sometimes developers use the word “libre” instead of “free” because in many romance languages it has the right connotation that’s missing from the english “free”. Think “free speech”, not “free beer”. Examples: Firefox, VLC.

“Open source” is a term that’s more nebulous. Depending on the specific software license it may or may not work like the “Free Software” above. It’s honestly a rather meaningless term these days.

The recipe above is the program’s “source code” - the human-readable programming that can be turned into a working program for a computer to run. Free software has a side benefit of allowing programmers to check for deliberately-planted security flaws. Such a check (often called a “security audit”) can take a long time and requires trusting the people doing the audit. But at least it’s theoretically possible to check for such flaws in free software. In closed proprietary software, checking for such deliberately planted flaws is far more difficult.

Free as in freedom not as in beer. https://en.m.wikipedia.org/wiki/Free_and_open-source_software