An airport accent is best defined as an accent that is hard to place. A person with an airport accent may pronounce some words with a British accent, while other words may be spoken with an American, Australian or any other accent you care to think of.
The reasons behind this may be as a result of having parents from different countries from the one the person was brought up in. Or it could be as a result of having lived in a variety of different places as a child, or a combination of the two. Either way the person may well have spent much of his life in airports, flying between the different countries.
"You have a very strong airport accent"
"Well I was born in Lebanon, but moved to England when I was 7, and then when we were 15 my family moved to America, but now I live in Paris"
"Yeah - and my parents are Russian and Brazilian - so we used to spent our summers in Moscow and our winters in Rio"
"That must have involved a lot of travelling"
"Yeah - I spent a lot of my youth in airports - my handwriting now resembles Frutiger."
"Shit a fucking brick"