Consider a good that exhibits a negative externality: cigarettes. As cigarettes are valued more by the individual than society, they can be considered to be demerit goods, and as a result the marginal social cost to society is greater than the marginal private cost, and this leas to overprovision of cigarettes in the free market.
Of the price of a cigarette in the UK, more than 75% is tax, and the reason taxes are used to resolve the externality is because they internalise the cost.
Say the gap between the marginal social cost and the marginal private cost was X, then by levying a tax of X on the cigarette producing company the firm will operate where marginal social benefit is equal to marginal social cost.
Taxes effectively push the marginal private cost to the left, creating an incentive for the company to reduce production.