What is the significance with woman keeping silent versus Esther's role for leadership?

Answer 1

If you mean by Esther the Queen Esther who (is claimed to have) lived during the Persian Empire around fifth century B.C.. The Old Testament speaks this tale.

Whether she was a real person or not, the story of her is a poignant tale.

At that time it was traditional women did not speak up. Even on The Bible is a sentence: "women should keep their peace in the church" (do not know the exact wording in English). That meant only men were allowed to discuss politics and lead. For women had no role in the world outside the home.

Esther was a Jewish orphan, who became the wife of the Persian king Ahasuerus (or Xerxes).
One time she learned that one of the noblemen was planning on to massacre all the Jewish people. Esther was not permitted to see the king unless he had asked for her, otherwise she could be put to death. She went to see the king anyways and was able to persuade him to give the Jewish people rights to carry arms and to defend themselves.

Basically she broke the glass ceiling and bent the kings ear, talking politics. The only reason she was not killed was because the king loved her.

The Jews established an annual feast of Purim in memory of their deliverance.

You ask what is the significance of women having same rights as men do? The significance of women taking active part in the politics and taking the lead?

It was world-changing when it happened, women took their place by men's side, not under their foot. It's the same significance as stopping slavery. It's a matter of equality, freedom, and self-esteem.