In MFL, Authentic assessment could be defined as an assessment of the way that the language is used, spoken or written, in a 'real' situation. For example, in September, when the students return from the holidays, I may ask them to write a letter of complaint to the hotel manager - they can relate to this as being 'genuine' or 'authentic' because some of them will have wanted to complain anyway, and the others will all be aware of times when a complaint could have been made.
Another authentic assessment would be a conversation with a native speaker of the target language; if the student and the 'subject' can both communicate effectively, then a real assessment can be made of the ability of the student, and good, clear feedback given.