The lining of your throat is swollen and irritated.
The air going by bothers it a lot making it think something very small is stuck in your throat causing you to cough.
The cough drop contains one of more of the following:
- Something like sugar that coats the throat so air doesn't irritate it.
- Something like menthol that reduces the swelling making it less irritated.
- Something that numbs the throat so it can't feel the air go by.
The really good but usually horribly tasting cough drops do all three.