The word used here for mighty one
is most often used in a military context and translated hero
or warrior,
as in Zephaniah 1:14. Thus, it usually refers to one who has distinguished himself as accomplishing heroic deeds, such as delivering his people from their enemies.1 It is used of both the Lord (Psalm 24:8; Isaiah 10:21; Isaiah 42:13; Jeremiah 14:9; Jeremiah 32:18; Zephaniah 3:17) and the Messiah (Psalm 45:3; Psalm 89:19; Isaiah 9:6).
In Zephaniah 3:17 it is accompanied by the verb to save
(יָשַׁע). That indicates that the deliverance in view shall come by divine activity; he is a warrior who will bring salvation. On the day of the Lord, he will triumph as a mighty one in his destroying the evil forces. He will secure peace for his remnant. Therefore, his people have no reason for fear except a fear of the Lord (Zephaniah 3:15–16).
17 The LORD your God is in your midst, a mighty one who will save; he will rejoice over you with gladness; he will quiet you by his love; he will exult over you with loud singing.