He will turn again, he will have compassion upon us; he will subdue our iniquities; and thou wilt cast all their sins into the depths of the sea.
He will turn again - to us, from having been turned away from us. Henceforth His "anger is turned away from" Israel; God Himself is turned to His people (Hosea 14:4).
He will subdue our iniquities - literally, tread under foot, as being hostile and deadly to us. Without subjugation of our bad propensities, even pardon could not give us peace. When God takes away the guilt of sin, that it may not condemn us, He takes away also the power of sin, that it may not rule us.
And thou wilt cast all their sins into the depths of the sea - never to rise again to view, buried out of sight in eternal oblivion; not merely at the shore side, where they may rise again. Compare Jeremiah 50:20, "In those days, and in that time, saith the Lord, the iniquity of Israel shall be sought for, and there shall be none: and the sins of Judah, and they shall not be found; for I will pardon them whom I reserve." As Israel's foe, Babylon-both the literal and the spiritual Babylon-shall sink to rise no more: like the stone cast by Seraiah into the Euphrates (in Jeremiah 51:61-64), and like "the great millstone" cast by the angel into the sea (in Revelation 18:21), so Israel's sins shall be "cast into the depths," never to rise against her.
Our ... their - change of person. Micah in the first case identifying himself and his sins with his people and their sins; in the second, speaking of them and their sins.