In his Sherashim, the Radak translates the word chafu as “fell,” as Haman was described before (Esther 6:12).
Targum and the Vilna Gaon translate chafu as “despondent or disappointed.”
The Ibn Ezra, however, sees the word as an active verb, meaning that somebody – in this case, Achashverosh’s servants – did this to him. This is due to their recognizing the king’s displeasure.
The Alshich explains that it was a Persian custom to cover the face of a capital offender.
In another example of mida kineged mida (“measure for measure”), the Me’am Loez cites an earlier verse (Esther 1:19) that this custom of covering was Haman’s own idea.
The Brisker Rav says that this detail was necessary because Charvona was at the end of the list of chamberlain advisers listed earlier (Esther 1:10), so he would have been too intimidated to speak against Haman earlier. With Haman’s face covered, he is able to speak, as he does in the next verse.