Airbnb is an online marketplace that connects people looking to rent out their homes or apartments with travelers seeking a place to stay. It was founded in 2008 and has since grown to become one of the world's largest hospitality companies.
The logo's font is likely Bello Script, an acclaimed brush typeface with numerous ligatures and swashes.
However, please note that in 2014, Airbnb introduced a new logo that was designed by London-based DesignStudio. The new logo incorporates a geometric sans serif font called LL Brown, which can be viewed here.