This verse, "and let them be ashamed of all their power and might, and let their strength be broken," expresses a prayer or declaration of the impotence of opposing forces. Let's break down the meaning:

"And let them be ashamed of all their power and might": This suggests that those who oppose the speaker or the group the speaker represents (in this case, the three holy children) rely on worldly power and strength. The prayer is that these opponents will ultimately be humbled and realize the inadequacy of their worldly power when faced with divine intervention or true righteousness. Shame, in this context, is not just about embarrassment, but a deep realization of the wrongness of their reliance on such things.

"And let their strength be broken": This is a plea or declaration that the power and capability of these opponents should be undermined or destroyed. It's a wish for their ability to inflict harm or exert influence to be neutralized. This can be interpreted literally (defeat in battle) or metaphorically (the breakdown of their oppressive system or ideology).

In the context of the Song of the Three Holy Children (also known as the Benedicite from the Book of Daniel):

The song is sung by Shadrach, Meshach, and Abednego while they are in the fiery furnace. They were thrown into the furnace by King Nebuchadnezzar for refusing to worship a golden idol. The song is a hymn of praise to God, and this particular verse expresses a desire for the downfall of the oppressive Babylonian power.

The verse is a confident statement that even though the King and Babylon have great power, God is greater, and their "might" and "strength" will ultimately fail. It's a declaration of faith in the face of persecution.

Therefore, the overall meaning is a prayer or pronouncement that those who rely on earthly power to oppose God or the righteous will be humbled and defeated. It emphasizes the ultimate supremacy of divine power over worldly power. It's a statement of faith, hope, and defiance in the face of oppression.