You can be profitable but still be burning cash in a few different ways. Profitable looks only at profit, not at cash flow, so it only means that "booked revenue in a year > booked costs in a year". Keep in mind that capital expenses are not costs, but are cash expenses. Also, some revenue in a given year might not be a cash transaction, because even if you booked it in that year, it might take much longer for you to actually get paid.
Some of the ways to burn cash:
(1) Expand operations: hiring people, hiring external services, leasing offices, leasing capacity, etc. All that happens far before any additional revenue comes in.
(2) Capex: capital expenses (buying servers, equipment, etc.) require cold, hard cash (or debt, which "costs" more than equity for a startup, so it is better to do equity funding).
(3) Working capital (current assets - current liabilities): some companies have positive (they receive the revenue cash before dispensing the costs cash) working capital, using their customers' money to expand the operations, others have negative working capital, requiring external funding to expand their operations.
My guess is that (2) and (3) don't apply for AirBnB, they are not a capital-intensive business, and as they get paid when the booking is done but pay out when the guest arrives, their working capital might actually be positive. So they probably need it to expand operations.