Upon arriving at the royal palace, Esther shows great courage in going to the king without being summoned. This would have been very difficult in any case, but in this particular situation it was absolutely crucial.
The king, who is named in the Bible as Ahasuerus or Xerxes, has been throwing extravagant parties to show off his power and wealth. At one of these events, the king promotes his highest official, Haman, an Agagite from Susa (Es. 3:1-2). But Mordecai, who is Jewish, refuses to bow down and pay homage to the king. This infuriates Haman and he sets out to eradicate not just Mordecai, but all Jews in the kingdom.
When Esther finds out about this plan, she approaches the king and asks him to revoke the edict that would exterminate all Jews. The king is initially hesitant, since an order of this magnitude cannot be reversed. However, he is persuaded to let her plead for her people.
Esther is able to convince the king that this is a matter of life and death for her and her people. But she does not simply tell him what she wants; she also invites him and Haman to a banquet the next evening. The rabbis explain that she did this for several reasons. The most obvious is that she wanted to get Haman at her side and expose him for his wicked intentions. Another reason is that she wanted to first win the kingโs confidence and trust.