FOSS stands for Free and Open Source Sofware.
“Open source” is rather self-explanatory, meaning the source code of the software is open, i. e. accessible.
The definition of “free” varies, two commonly used variants are gratis (no monetary cost, “free as in beer”) and libre (minimal restrictions, “free as in freedom”). The distinction usually lies in the kinds of rights offered to the end-user, which can range from the right to use the software to the rights to access its source code, modify and redistribute it.
What rights does the end-user have with certain software depends on the license they received said software under.
Something released into the public domain (not just published in the open, but with an explicit waiver such as the Unlicense) would grant all the rights that are applicable to that software, including the right to use (commercially or not), redistribute and modify in any way.
A popular license in the FOSS world is GPL, which is frequently violated, as it mandates that the source code of any modified versions of the software must be disclosed along with these versions for as long as they’re offered to the public (not necessarily for free; the license mandates that source be made available at least in the same way the software itself was provided at no additional cost). Linux kernel is probably the most popular project licensed in this way.