The word “fiat” means an official decree or to give sanction to something. In Latin it means “let there be” or “let it happen/exist.” For example, in Genesis when God said “Let there be light” the Latin phrase is “fiat lux.”
The word in common language has become a kind of “catch all” word to describe a permission received or a rule given.
Mary’s response to the angel was a “fiat” statement: “Behold, I am the handmaid of the Lord. May it be done to me according to your word.” Or in Latin: “dixit autem Maria ecce ancilla Domini **fiat **mihi secundum verbum tuum et discessit ab illa angelus”
When we refer to Mary’s fiat we are referring to Mary’s submission to the will of God.