What did Hashem mean when He said that all the nations of the world will be blessed through him?
Targum Yonasan: He meant that all the nations would be blessed on the merit of his children (thanks to Avraham, who listened to His voice) 1 .
Seforno: When all the nations of the world will call out in the Name of Hashem to serve Him, they will be blessed via Avraham's children, and they will try to emulate them. 2
What has the aforementioned Berachah got to do with the fact that Avraham listened to Hashem's Voice?
Seforno: Because one Mitzvah leads to another. It is because Avraham listened to Hashem that some of his children will teach the Nations of the world how to serve Hashem; and this in turn, will be a merit for Avraham.