possessing overwhelming, awe-commanding power; mighty and majestic enough to master every rival
This word points to power so great that it compels awe, not to beauty or mere size. Whatever it describes is overwhelming: the sea that drowns sailors, the towering cedar whose fall shakes a nation, the king no one can resist, and above all the God whose raised hand shattered Pharaoh's army. The note is force, not decoration.
Because it is a word of overpowering strength, it almost always sets one power over against others. When the poet calls the raging waters mighty and then calls God mightier still on high (Psalm 93:4), the whole point is that God overmasters even the strongest rival. Israel's poets used it to crown the LORD as the incomparable king and warrior, taking up the very title that neighboring peoples gave their own gods and claiming it for the LORD alone.
From this same idea the word also names people who hold overwhelming rank: chieftains, nobles, and magnates. In the later books it hardened into an almost official label for the aristocracy, such as the nobles of Tekoa who would not stoop to the wall work in Nehemiah's day. The connection is direct: a mighty one is simply a person who embodies the same commanding power the word describes everywhere else.