When economists speak of a public good they typically mean a good which has certain properties, whether it is provided publicly (by a government) or provided privately. The properties which make a good public are non-rivalness in consumption and non-excludability.
By non-rivalness in consumption we mean a good which can be shared by many people without being "used up." An excellent modern example is a website. Clearly you can (and are) sharing this and other websites with many other users. Yet your experience in using the site is almost identical whether you are the only person using the site there are thousands. Other examples of goods which are pure or almost purely non-rival include statues, national defense, and clean air.
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