What is the army of two hundred million?
The army of two hundred million is the massive horde of horsemen released at the sounding of the sixth trumpet, led by four angels loosed from the Euphrates River, given the mission to kill a third of mankind.
When the sixth angel sounds his trumpet, a voice comes from the four horns of the golden altar before God, commanding that four angels bound in the great river Euphrates be loosed. These four angels had been held there and were prepared for a specific hour, day, month, and year, with one terrible assignment: to slay a third of mankind. Once released, they lead this vast army of two hundred million horsemen, or two hundred thousand thousand, into their work of judgment.
The riders and horses are described in striking and fearsome detail. The riders wear breastplates of fire, jacinth, and brimstone. The horses have heads like lions, and out of their mouths come fire, smoke, and brimstone, three plagues by which a third of men are killed. Their power is not only in their mouths but also in their tails, which are like serpents with heads, able to inflict harm. This description alone makes clear that this is not an army made up of ordinary earthly soldiers; the fact that they are led by four angelic beings confirms that this army is otherworldly in nature.
Joel 2:1 to 11 is brought in to corroborate this picture of an unprecedented army connected to the day of the Lord. Joel describes a great and strong people, unlike any that has ever been or ever will be again, whose appearance is like horses and horsemen, with fire devouring before them, causing the earth to quake and the heavens to tremble. Importantly, Joel shows that the Lord Himself utters His voice before this army, for it is His camp, and He is the one strong enough to execute His word. This tells us these are warriors carrying out God's command to execute judgment on the earth, not creatures serving Satan.
Despite the horror and devastation caused by this army, and though a third of mankind is killed by the plagues of fire, smoke, and brimstone, those who survive still do not repent. They continue worshiping devils and idols of gold, silver, brass, stone, and wood, objects that cannot see, hear, or walk, and they do not turn from their murders, sorceries, fornication, or thefts. This shows that even severe judgment does not automatically produce repentance in unbelieving hearts, and it is noted that since the Church is still on the earth at this point, the mystery of God is not yet finished, meaning people are still able to repent and receive salvation through belief in Jesus Christ, even though most who survived these plagues refused to do so.
The scriptures
And the sixth angel sounded, and I heard a voice from the four horns of the golden altar which is before God, Saying to the sixth angel which had the trumpet, Loose the four angels which are bound in the great river Euphrates. And the four angels were loosed, which were prepared for an hour, and a day, and a month, and a year, for to slay the third part of men. And the number of the army of the horsemen were two hundred thousand thousand: and I heard the number of them. And thus I saw the horses in the vision, and them that sat on them, having breastplates of fire, and of jacinth, and brimstone: and the heads of the horses were as the heads of lions; and out of their mouths issued fire and smoke and brimstone. By these three was the third part of men killed, by the fire, and by the smoke, and by the brimstone, which issued out of their mouths. For their power is in their mouth, and in their tails: for their tails were like unto serpents, and had heads, and with them they do hurt. And the rest of the men which were not killed by these plagues yet repented not of the works of their hands, that they should not worship devils, and idols of gold, and silver, and brass, and stone, and of wood: which neither can see, nor hear, nor walk: Neither repented they of their murders, nor of their sorceries, nor of their fornication, nor of their thefts.
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. A fire devoureth before them; and behind them a flame burneth: the land is as the garden of Eden before them, and behind them a desolate wilderness; yea, and nothing shall escape them. The appearance of them is as the appearance of horses; and as horsemen, so shall they run. Like the noise of chariots on the tops of mountains shall they leap, like the noise of a flame of fire that devoureth the stubble, as a strong people set in battle array. Before their face the people shall be much pained: all faces shall gather blackness. They shall run like mighty men; they shall climb the wall like men of war; and they shall march every one on his ways, and they shall not break their ranks: Neither shall one thrust another; they shall walk every one in his path: and when they fall upon the sword, they shall not be wounded. They shall run to and fro in the city; they shall run upon the wall, they shall climb up upon the houses; they shall enter in at the windows like a thief. The earth shall quake before them; the heavens shall tremble: the sun and the moon shall be dark, and the stars shall withdraw their shining: And the LORD shall utter his voice before his army: for his camp is very great: for he is strong that executeth his word: for the day of the LORD is great and very terrible; and who can abide it?
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.