This is an idiom. AT: "When Peter became fully awake and alert" or "When Peter became aware that what had happened was real" (See: [[rc://en/ta/man/translate/figs-idiom]])
Here "the hand of Herod" refers to "Herod's hold" or "Herod's plans." AT: "brought me from the harm Herod had planned for me" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here "the people of the Jews" probably referred mainly to the Jewish leaders. AT: "all that the Jewish leaders thought would happen to me" (See: [[rc://en/ta/man/translate/figs-synecdoche]])