“ And now, my daughter, don't be afraid. I will do to you all that you say, for all the city (literally ‘the gate') of my people know that you are a worthy woman.”
He then assured her that as far as it lay within his power he would do what she had requested, because she had a reputation among all the people of Bethlehem as being a worthy woman. ‘All the gate of my people.' The gate was the place where people met and conversed, and where the elders made decisions and judged the rights and wrongs of people. Thus her reputation was good among the people, and equally among those most competent to judge.
There is a play on words here in that Boaz had been declared to be ‘a man of chayil (wealth)', see Ruth 2:1, and now Ruth is declared to be ‘a woman of chayil (worthiness)'. Both were getting a good bargain.