What is an example of an externality associated with having an airport built near your home?
First, we must remember that there are both positive and negative externalities. Negative externalities are costs imposed on you by, in this case, having an airport near your home. Positive externalities are benefits that you get from having the airport there.
Most people would think more about the negative externalities of having an airport near their home. The obvious example of this is the noise. At a busy airport, airplanes are taking off and landing all the time. This causes a lot of noise, sometimes at very inconvenient times. This is a cost that is imposed on you even if it is not really a monetary cost.
However, there are some positives that could come out of having the airport there. The most likely positive externality is that there will be more amenities near your home. For example, it is at least possible that there will be more restaurants near your home than there would be if the airport were not there. It will also be easier for you to travel in the event that you want to go by air.