What is Public Good?

Legal Definition
In economics, a public good is a good that is both non-excludable and non-rivalrous in that individuals cannot be effectively excluded from use and where use by one individual does not reduce availability to others.[1] Gravelle and Rees: "The defining characteristic of a public good is that consumption of it by one individual does not actually or potentially reduce the amount available to be consumed by another individual." In a non-economic sense, the term is often used to describe something that is useful for the public generally, such as education and infrastructure, although these are not "public goods" in the economic sense. This is in contrast to a common good which is non-excludable but is rivalrous to a certain degree.
-- Wikipedia
Legal Definition
In economics, a public good is a good that is both non-excludable and non-rivalrous in that individuals cannot be effectively excluded from use and where use by one individual does not reduce availability to others. Gravelle and Rees: "The defining characteristic of a public good is that consumption of it by one individual does not actually or potentially reduce the amount available to be consumed by another individual." In a non-economic sense, the term is often used to describe something that is useful for the public generally, such as education and infrastructure, although these are not "public goods" in the economic sense. This is in contrast to a common good which is non-excludable but is rivalrous to a certain degree.

Public goods include fresh air, knowledge, official statistics, national security, common language(s), flood control systems, lighthouses, and street lighting. Public goods that are available everywhere are sometimes referred to as global public goods. There is an important conceptual difference between the sense of 'a' public good, or public 'goods' in economics, and the more generalized idea of 'the public good' (or common good, or public interest),"‘the’ public good is a shorthand signal for shared benefit at a societal level [this] (philosophical/political) sense should not be reduced to the established specific (economic) sense of ‘a’ public good."

Many public goods may at times be subject to excessive use resulting in negative externalities affecting all users; for example air pollution and traffic congestion. Public goods problems are often closely related to the "free-rider" problem, in which people not paying for the good may continue to access it. Thus, the good may be under-produced, overused or degraded. Public goods may also become subject to restrictions on access and may then be considered to be club goods or private goods; exclusion mechanisms include copyright, patents, congestion pricing, and pay television.

There is a good deal of debate and literature on how to measure the significance of public goods problems in an economy, and to identify the best remedies.
-- Wikipedia
Legal Definition
An item that taxation is used to finance, the consumption of which has been decided by the whole of society. It is not an item for consumption that an individual has decided upon.