What is the darkness on the kingdom of the beast?
When the fifth angel pours out his vial upon the seat of the beast, his kingdom is plunged into a total, thick darkness, and the people suffer such pain from their sores that they gnaw their tongues yet still refuse to repent.
The fifth vial is poured out directly upon the seat, or throne, of the beast, and the result is that his whole kingdom becomes full of darkness. This is not a partial dimming of light but a complete and oppressive darkness that brings intense misery. The people under this judgment gnaw their tongues in pain, and instead of turning to God they blaspheme the God of heaven because of their pains and their sores, still refusing to repent of their deeds.
This darkness echoes the darkness that fell upon Egypt in the days of Moses, when the Lord stretched out darkness over the land so thick it could be felt, so thick that people could not even see one another or rise from where they sat for three days. Lamentations describes a similar experience of being led into darkness and not light because of the rod of God's wrath, showing that this kind of judgment darkness has always been connected with affliction and suffering under God's hand.
Other scriptures describe this same day as one of gloominess and thick darkness, a day unlike any that has ever been or ever will be again, when the sun is darkened, the moon gives no light, and men stumble about like the blind because of their sin against the Lord. Jeremiah warns people to give glory to God before He causes this darkness, before their feet stumble on the dark mountains and the light they look for turns instead into the shadow of death and gross darkness. So the darkness on the beast's kingdom is a real, tangible, and terrifying judgment that leaves the wicked in torment with no relief, and yet even then their hearts remain hardened against God.
The darkness on the beast's kingdom stands alongside the sores from the earlier vial, meaning that at this point the people are suffering in complete blackness while their bodies are still afflicted with painful ulcers. There is no relief for them in this state, only compounded misery, and still, tragically, no repentance follows.
The scriptures
And the fifth angel poured out his vial upon the seat of the beast; and his kingdom was full of darkness; and they gnawed their tongues for pain, And blasphemed the God of heaven because of their pains and their sores, and repented not of their deeds.
I AM the man that hath seen affliction by the rod of his wrath. He hath led me, and brought me into darkness, but not into light.
And the LORD said unto Moses, Stretch out thine hand toward heaven, that there may be darkness over the land of Egypt, even darkness which may be felt. And Moses stretched forth his hand toward heaven; and there was a thick darkness in all the land of Egypt three days: They saw not one another, neither rose any from his place for three days: but all the children of Israel had light in their dwellings.
Blow ye the trumpet in Zion, and sound an alarm in my holy mountain: let all the inhabitants of the land tremble: for the day of the LORD cometh, for it is nigh at hand; A day of darkness and of gloominess, a day of clouds and of thick darkness, as the morning spread upon the mountains: a great people and a strong; there hath not been ever the like, neither shall be any more after it, even to the years of many generations.
Behold, the day of the LORD cometh, cruel both with wrath and fierce anger, to lay the land desolate: and he shall destroy the sinners thereof out of it. For the stars of heaven and the constellations thereof shall not give their light: the sun shall be darkened in his going forth, and the moon shall not cause her light to shine.
The great day of the LORD is near, it is near, and hasteth greatly, even the voice of the day of the LORD: the mighty man shall cry there bitterly. That day is a day of wrath, a day of trouble and distress, a day of wasteness and desolation, a day of darkness and gloominess, a day of clouds and thick darkness, A day of the trumpet and alarm against the fenced cities, and against the high towers. And I will bring distress upon men, that they shall walk like blind men, because they have sinned against the LORD: and their blood shall be poured out as dust, and their flesh as the dung.
Give glory to the LORD your God, before he cause darkness, and before your feet stumble upon the dark mountains, and, while ye look for light, he turn it into the shadow of death, and make it gross darkness.
Woe unto you that desire the day of the LORD! to what end is it for you? the day of the LORD is darkness, and not light. As if a man did flee from a lion, and a bear met him; or went into the house, and leaned his hand on the wall, and a serpent bit him. Shall not the day of the LORD be darkness, and not light? even very dark, and no brightness in it?
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.