# signet ring
This ring had the king's name or mark on it. When he put a wax seal on important papers, he would press the mark onto the seal. See how you translated this in Esther 3:10.
# gave it to Mordecai
By giving his signet ring to Mordecai, the king gave Mordecai the authority to write important papers that people would have to obey.
# Haman's estate
This refers to the things that had belonged to Haman and that the king had given to Esther.