Why do we use definite article in the sentence: I went to the airport at 8 o'clock.
when this airport is mentioned for the first time?
That seems to be just a convention - with no clear explanation why! Remember that much in language is idiomatic and cannot be readily explained.
There are differences, too, depending on countries/cultures. In the US, we say, "He was in the hospital overnight," but in England, it's phrased, "He was in hospital ... "