What are the ten horns and the ten kings?
The ten horns represent ten kings who have not yet received a kingdom but who are given power to reign as kings for one hour together with the beast; they unite in purpose to give their strength to the beast and make war against the Lamb.
Scripture describes the ten horns as ten kings who, at the time John sees the vision, have not yet received a kingdom of their own. Instead, they are given authority to reign as kings for a brief period, described as "one hour," alongside the beast. They are not independent rulers acting on their own agendas but are joined together with the beast in his final campaign.
These ten kings have one mind and purpose. Rather than competing with the beast for power, they willingly give their own power and strength over to him, making themselves extensions of his authority. This shows a complete unity of will among them, all working toward the same end under the beast's leadership.
Together with the beast, these ten kings make war against the Lamb. But their combined strength is no match for Christ, for he is Lord of lords and King of kings. The Lamb overcomes them, along with all who are with him, who are described as called, chosen, and faithful. This is part of the larger picture of the beast's final defeat, which culminates in the battle of Armageddon, where the armies gathered by the beast and these kings are destroyed by the Lord.
The scriptures
And the ten horns which thou sawest are ten kings, which have received no kingdom as yet; but receive power as kings one hour with the beast. These have one mind, and shall give their power and strength unto the beast. These shall make war with the Lamb, and the Lamb shall overcome them: for he is Lord of lords, and King of kings: and they that are with him are called, and chosen, and faithful.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.