Esther's First Banquet (Esther 5) December 7
When Esther goes in to see the king, he is receptive to her—she would not die. Xerxes knows that she must have some important reason for daring to approach him, and he reassures her of his favor, promising her up to half his kingdom—"probably an example of Oriental [i.e. Middle Eastern] courtesy that was not intended to be taken too literally (cf. Mark 6:23)" (Expositor's Bible Commentary, note on Esther 5:3).
Esther's response is not to immediately plead for her people. Instead, she invites the king and Haman to a banquet she has prepared for that day. Given the presumptuousness of her entrance, she may not have deemed it a good moment to compound the problem by possibly upsetting the volatile king in revealing that she, his wife and queen, had for all this time not disclosed her national identity to him. It could also be that she did not want to reveal this matter before all the royal officials who were probably present. But why invite Haman to the banquet? "Many suggestions have been made. To make Xerxes jealous. Perhaps so that Haman's reaction, when Esther accuses him, might reveal his guilt. Perhaps Esther acted in the best traditions of her people, to confront Haman face-to-face rather than speak behind his back" (Bible Reader's Companion, note on verse 4).
Xerxes realizes that Esther did not risk her life for a mere banquet. And he probably understood that she prepared the banquet so as to avoid discussing the real reason before all of his officials. At the meal, then, the king asks her for her actual petition. But she delays, asking the two back for a second banquet the next day—which, remarkably, the king does not question. "One may ask why Esther waited instead of disclosing what was on her mind. [Whatever her reason,] the delay providentially allowed time for the king's sleepless night and the events that followed (ch. 6)" (Nelson Study Bible, note on verses 6-8).
Haman's brief exultation is cut short by Mordecai's disrespect (verse 9). His vanity caused him such hatred for Mordecai that he could not enjoy how well things seemed to be going for him (verses 10-13). Of course, in this case things were not going so well as he thought. "Haman's boasting only accentuated his later humiliation and fall from favor (cf. Prov 16:18)" (Expositor's Bible Commentary, note on Esther 5:11-12).
The "hanging" proposed for Mordecai was, as the Word in Life Bible points out in a note on Esther 2:23, "probably not hanging as we know it. The gallows of ancient Persia was not a scaffold but a pole or stake upon which the victim was impaled. Execution by such impalement was a common practice of the Assyrians, who killed war captives by forcing their living bodies down onto pointed stakes. The Persians continued this grim means of execution. Thus references to hanging in Esther (5.14; 6.4; 9.14) probably refer to impalement, or possibly crucifixion."