In the verse, Esther asks Mordecai to gather with all the Jews in Susa and asks them to fast for her for three days and three nights. Fasting was a common practice in ancient times that was used as a way to demonstrate devotion and repentance to God, it was also used as a means to seek God's help in difficult situations or to ask for His protection.
Fasting is an expression of faith and trust in God. Esther was willing to risk her life to save her people, she knew that without God's help this task would be impossible. Faith in God prompted her to make this decision. She put herself in the hands of the Lord so that He would do whatever was necessary to save his people.