Air pollution is what economists call a "negative externality" or, as in the link below, a "external diseconomy." This is defined in the link as a
cost arising from an economic activity which does not fall on the person or firm controlling the activity.
When air pollution happens, it is not necessarily those who pollute who have to pay the costs. This is a major economic impact of pollution.
For example, one impact of air pollution is an increased need for health care. When people breathe polluted air too much, they often end up with respiratory problems and need medical treatment. They have to (or their insurers do) pay for the effects of air pollution even if they did not cause it.
Air pollution can have more widespread economic impacts when or if governments try to reduce it. Governments then have to impose regulations on firms, forcing them to pollute less. In the short term, at least, these regulations make those firms' costs go up and that reduces the supply of whatever those firms produce. This is a major reason why air pollution (greenhouse gasses are a huge example of this) is not better regulated by the government.
Air pollution, then, can economically impact both individuals and whole economies.