This verse from 1 Esdras 4:61 is a concluding statement in the story of Zerubbabel winning a philosophical contest before King Darius. Let's break it down:

"And so he took the letters..." The "letters" refer to official documents or decrees given to Zerubbabel by King Darius, confirming his victory and authorizing his requests, likely relating to rebuilding the Temple in Jerusalem and allowing the Jews to return to their homeland. These letters are the tangible outcome of his success.

"...and went out, and came to Babylon..." Zerubbabel departs from the court of King Darius (presumably in Persia) and travels to Babylon. Babylon, even after the Persian conquest, remained a significant center of Jewish population. It was a major hub for the Jewish diaspora.

"...and told it all his kindred." In Babylon, Zerubbabel shares the news of his victory and the contents of the letters with his family and extended community (his "kindred"). This is a moment of great joy and hope. It signifies that their prayers have been answered, that the rebuilding of the Temple and the return to Jerusalem are now officially sanctioned. He's sharing the good news and likely preparing for the journey back to their ancestral homeland.

In essence, the verse means that Zerubbabel, after winning a great favor from the king, went to Babylon and delivered the good news and official documents to his family and community, signifying the beginning of the fulfillment of their hopes for restoration. The verse suggests the following:

Validation: His efforts were successful and recognized by the ruling power.
Communication: Zerubbabel prioritizes informing his people, especially his family and those living in exile, of the positive developments.
Hope: The news brings renewed hope for the restoration of the Jewish people and their religious center in Jerusalem.
Preparation: This is the signal for the community to prepare for a return to their homeland and the immense task of rebuilding.