What does "Let us break their bands asunder" mean?
It means rebellious humanity rejecting God's sovereign rule over them. Jew and Gentile alike declare they will not let God govern their affairs; they cast away His cords of authority and refuse Christ as the King who came to set up the Kingdom.
Les explains that the cry “Let us break their bands asunder” is aimed at the Godhead: it means, “Let’s not let God rule in our affairs.” The next phrase, “cast away their cords,” describes rejecting God’s sovereign rule. In the context, Jew and Gentile alike—the heathen and the rulers of Israel—took counsel against the Anointed. Although Acts lays blame on Israel for crucifying Christ, Rome carried it out; Pilate made the decree, so Israel and the Romans together turned against Him. Christ had come to proclaim that He was the King, ready to set up the Kingdom, but both Jew and Gentile said, “No way, we’ll not have this man to rule over us.” God the Father in heaven then laughs and holds the nations and Israel in derision.