"adjective below or contrary to the standards expected in a particular profession"
But it is always being used in situations where there is no profession as such. IE a shop manager or a florist for example cannot officially be unprofessional for example. But more importantly (and less pedantically) than that, it seems to have been extended to cover anything that the user of the word doesn't happen to like. For example a shop assistant who talks to someone else whilst serving a customer is 'unprofessional', whereast IMO the relevant and perfectly adequate word is 'rude'.