Question about airports (White Giant)

Recently an airport showed up in one of my countries.

It wasn't military related at all....it was just an airport and shows up in a completely different category when I look at "changing icons."

Recently, I also built an Air transport corp in this country? Does this have anything to do with the new airport? What use does this type of airport provide?

yes, you are 100% correct. when you built an air transport corp, you in essence built an airport. It is used for the same things real life airports are used for....transporting people and frieght

You don't build an airport... When you build an Air Transport corp, your country automatically issues the order to buy an Airport. Difference from what Gaius said is that you have to pay for the Airport, plus the 100B for the new corp.