Not Airbnb. Your potential hosts. Airbnb allows you to provide multiple means of proving you're reasonable. Linking your FB profile is one way. Airbnb will then show the number of friends you have.

This may have changed since when I signed up years ago.

It's just like your GitHub is a reputation aid when applying for a job. It's not required but what you have on there can help.

EDIT: In case it isn't clear, I'm not claiming here that Airbnb is forming some sort of transcontinental people database.