The effect a tax has on the distribution of economic welfare. Tax Incidence describes how the burden of a tax is shared among producers and consumers in a market.
Assume a new per unit tax of 1$ is imposed on ice cream. As a result, producers increase the price of ice cream from 2$ to 3$. At first view, it may seem as if consumers have to bear the entire burden of the tax. However, some buyers may decide not to buy ice cream for 3$, because that is too expensive for them. As a result, total revenue received by the producers will fall (since they do not receive the additional tax revenue). In other words, unless demand is perfectly unelastic, consumers and producers will usually share the burden of a tax, at least to a certain degree. To see how to calculate tax incidence, check out this article.
Looking at the tax incidence can help policy makers to measure the actual impact of a tax. This is important, because imposing a tax on a certain actor does not necessarily mean that this actor will also bear the resulting burden. Therefore it is essential for policy makers to look at the tax incidence in order impose taxes in the best interest for society.