What is a Pigouvian Tax?

In the dynamics of a certain market, it would be externalities as a consequence of the normal operation of buying and selling of this market. An externality happens when a third-party (not involved in the operation) is affected positively or negatively by market activity. The perfect example of this is environmental contamination. Let's think in a coal extractor company. When the company does its main activity, it generates CO2 contamination and affects the water supplies within a certain area. We can call this as NEGATIVE EXTERNALITY because people near its operation area will be affected by the company’s procedures (e.g. health issues for contaminating air or water). (There are also POSITIVE EXTERNALITIES like Electric Cars Market. When a normal car is replaced by one of those; it impacts the environment in a positive way).
In the 20’s, the British Economics Arthur Pigou states that those externalities cannot be corrected by market solely. That is why, the companies only pursuit their profit maximisation. For this reason, Pigou believed that the regulator must implement a tax (or a subsidy in positive externalities) to change the market equilibrium and reduce (or increase) the traded quantity. When the externality is negative, a tax raises the market price and reduces quantity sold (via demand and supply). On the other hand, when the externality is positive, a subsidy reduces the market price and rise traded quantity. For this argument, this kind of taxes is called Pigouvian taxes.
In conclusion, Pigouvian taxes are taxes implemented to reduce a negative externality and the impact of a certain market on a third party, using the price to reduce the size of that market. There is also Pigouvian subsidy, which is implemented to raise a positive externality in the same way.