What did HaSh-m mean when He said that, "all the nations of the world would be blessed through Avraham"?
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 HaSh-m to serve Him, they will be blessed via Avraham's children, and they will try to emulate them. 2
It is in connection with this blessing that Yitzchak blessed Yaakov in that it was via his children that it should be fulfilled (Rashi to Bereishis 29:4); refer to 26:3:7:2.
What does this have to do with the fact that Avraham listened to HaSh-m's Voice?
Seforno: Because one Mitzvah leads to another. It is because Avraham listened to HaSh-m that some of his children will teach the Nations of the world how to serve HaSh-m; and this in turn, will be a merit for Avraham.
