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Proprietary (or Non-free) is anything that is under a restrictive license. This term can be used by both the Free Software Foundation followers, and members of the Open Source community for a vague term. For a more precise term, both fields of thought use their own concrete definitions. The Free Software Foundation followers use the term Non-free or proprietary, while members of the Open Source community use the term Closed-Sourced. Both non-free and closed-source have similar, yet different meanings. Both terms, however, can be replaced with proprietary when being general.
Most proprietary programs can be identified by the program having an EULA to accept. Most likely you won't read the EULA because you're a dirty normie, but having to accept an EULA is the clearest sign of the program being proprietary. To check out licenses that aren't proprietary, go to the Licenses page and read about free software licenses. Free software licenses can be identified by the header of the license file while proprietary licenses cannot be identified without reading at least a couple pages.