The phrase "fervent prayers" means extremely passionate and strong prayers. It refers to praying with great intensity, ardor, and sincerity. Full definition
We are told in the Bible that «The effectual fervent prayer of a righteous man availeth much,» or as it is put in the more meaningful Revised Standard Version, «The prayer of a righteous man has great power in its effects.» (religion-online.org)
In any event, Hezekiah spreads the written threats of the Assyrians before the LORD in the temple with fervent prayer, Isaiah utters a defiant oracle of victory, a great disaster befalls the Assyrian army, Sennacherib returns to Nineveh, and Jerusalem is saved. (religion-online.org)