Jamieson, Fausset and Brown on Isaiah 51:4

4. my people--the Jews. This reading is better than that of Gesenius: "O peoples ... nations," namely, the Gentiles. The Jews are called on to hear and rejoice in the extension of the true religion to the nations; for, at the first preaching of the Gospel, as in the final age to come, it was from Jerusalem that the gospel law was, and is, to go forth (Is 2:3).

law ... judgment--the gospel dispensation and institutions (Is 42:1, "judgment").

make ... to rest--establish firmly; found.

light, &c.--(Is 42:6).