What does the word “fiat” mean in the Bible?

The word “fiat” is Latin, and it means “let it be done.” Mary’s fiat was when she said, “Behold, I am the handmaid of the Lord; let it be to me according to your word” (Luke 1:38).

What does Mary's fiat mean?

Pope St. John Paul II said,

Mary's words at the Annunciation "I am the handmaid of the Lord; let it be to me according to your word" (Lk 1:38), indicate an attitude characteristic of Jewish piety. At the beginning of the Old Covenant, Moses, in response to the Lord's call, proclaims himself his servant (cf. Ex 4:10; 14:31).
With the coming of the New Covenant, Mary also responds to God with an act of free submission and conscious abandonment to his will, showing her complete availability to be the "handmaid of the Lord."
Mary, "full of grace," by proclaiming herself "handmaid of the Lord" intends to commit herself to fulfil personally and in a perfect manner the service God expects of all his people.