1. free from difficulties or financially solvent
To be 'afloat' in a literal sense means to be floating on water. Figuratively, it means to avoid being consumed by a difficult situation, particularly a financial or work-related one. If you have, at least for the time being, enough money to operate as normal and pay your debts, then you can be said to be 'afloat.' It is used in a social and professional context, but is more common in the latter. A similar expression is 'keep your head above water.'
2. floating on water
This definition is the literal meaning of the word and would only be used in a social context.