The beast coming out of the sea is a man who will be revealed at the beginning of the tribulation period, destined to conquer the world (rider of the white horse in 6:2): he will initially subdue three kings in a confederation of ten (Dan.7:24-26, Rev.17:12-13), and will proceed to conquer the others, obtaining a total dominion after three and a half years. He is also known as the Antichrist (I John 2:18), the Assyrian (Isa.10:24, 31:8, Mic.5:5), king of Babylon (Isa.14:4), Gog (Eze. 38:18), the Little Horn (Dan. 7:8), the Stern Faced King (Dan.8:23), the Ruler Who Will Come (Dan.9:26-27), a Contemptible Person (Dan.11:21), the Wicked (Isa.11:4), and the Lawless One (II Thes.2:8).
His name is not given, but it corresponds with the number 666. All 22 letters of the Hebrew alphabet have a number equivalent, so Hebrew names also have a numerical equivalent. The numerical value of the name of the Antichrist will be 666; due to the great number of possible combinations, he can only be identified once his name is known.
His heads and horns correspond with those of the dragon (Rev.12:3), indicating the affinity of the two: the beast receives his power, his throne and great authority from the dragon; in effect, after being hurled on earth, Satan gives the Antichrist power to overcome the remaining seven kings, and uses the Antichrist as his agent to make war against the saints. They are both objects of worship as from the middle of the tribulation period.
Whilst on the dragon the diadems were seen on his heads (spiritual conquest), on the beast they are on his horns (political conquest). The leopard is a symbol of Greece, the bear of Medo-Persia, the lion of Babylon (Daniel 7:4-6): the three empires dominating over Israel since Daniel until the Romans, who were allowed to live for a season and a time (Daniel 7:12), which may mean that their religion, culture, and military character will be incorporated in the beast.
Based on Revelation 17:9,10, the seven heads also represent seven kings (or kingdoms), of which five have fallen, one is (at the time of John), the other has not yet come. If they refer to the gentile dominion over the Jews, the first five are Egypt, Assyria, Babylon, Medo-Persia and Greece. In John's time it was Rome. Still to come is the Antichrist heading a federation of ten nations.
The wounded head is likely to be the Antichrist himself, whom Satan will apparently revive after a mortal wound, to the astonishment of the world. At this time (mid-tribulation) he was allowed to boast and blaspheme, to fight and conquer the saints (the faithful Jews), and to receive worship from the unsaved throughout the whole world, for three and a half years until the end of this period (Daniel 7:8,20,21,24-26). Verses 9 and 10 are an encouragement to those who suffer loss of liberty, even life, because of their faith in Christ, to persevere with patience and faithfulness, particularly at that time.
The beast coming out of the earth has two horns, looking like a lamb (gentle) but speaking like a dragon (deceitfully). It is a religious man, a priest, called later the false prophet (Rev.16:13, 19:20, 20:10), and like the Antichrist, he comes from the Gentile nations: sea and earth have the same meaning (Daniel 7:3 and 17). These two make a terrible couple, and the Lord Jesus had warned of the coming of false christs and false prophets in the last days.
Whilst the Antichrist exalts himself, even to the point of displaying himself as God, the False Prophet, who is not a political leader, promotes the Antichrist. The Antichrist will delegate all his power to him in his presence, so that the False Prophet will perform extraordinary signs, and deceive all so that they make an image of the Antichrist (like Nebuchadnezzar - Daniel 3), endowing him with intelligence, speech, and power to kill those who do not submit and worship him.
Every person on earth will be required to receive the mark, name or number of the Antichrist, imprinted on their right hand or on their forehead, thus acknowledging that he is their lord and master. This is obligatory for any trading, purchase or sale.
The number six is the number of man: it is imperfect, being short of the perfect seven. Adam was created on the sixth day of the week, and there are various instances in the Bible where the imperfect 6 indicates human power, for example: Goliath's height was 6 cubits, his iron spearhead weighed six hundred shekels (1 Samuel 17:4,7); the image of Nebuchadnezzar was sixty cubits high and six cubits wide (Daniel 3:1).
The Beast from the Sea
1 Then I stood on the sand of the sea. And I saw a beast rising up out of the sea, having seven heads and ten horns, and on his horns ten crowns, and on his heads a blasphemous name.
2 Now the beast which I saw was like a leopard, his feet were like the feet of a bear, and his mouth like the mouth of a lion. The dragon gave him his power, his throne, and great authority.
3 And I saw one of his heads as if it had been mortally wounded, and his deadly wound was healed. And all the world marvelled and followed the beast.
4 So they worshiped the dragon who gave authority to the beast; and they worshiped the beast, saying, "Who is like the beast? Who is able to make war with him?"
5 And he was given a mouth speaking great things and blasphemies, and he was given authority to continue for forty-two months.
6 Then he opened his mouth in blasphemy against God, to blaspheme His name, His tabernacle, and those who dwell in heaven.
7 It was granted to him to make war with the saints and to overcome them. And authority was given him over every tribe, tongue, and nation.
8 All who dwell on the earth will worship him, whose names have not been written in the Book of Life of the Lamb slain from the foundation of the world.
9 If anyone has an ear, let him hear.
10 He who leads into captivity shall go into captivity; he who kills with the sword must be killed with the sword. Here is the patience and the faith of the saints.
The Beast from the Earth
11 Then I saw another beast coming up out of the earth, and he had two horns like a lamb and spoke like a dragon.
12 And he exercises all the authority of the first beast in his presence, and causes the earth and those who dwell in it to worship the first beast, whose deadly wound was healed.
13 He performs great signs, so that he even makes fire come down from heaven on the earth in the sight of men.
14 And he deceives those who dwell on the earth by those signs which he was granted to do in the sight of the beast, telling those who dwell on the earth to make an image to the beast who was wounded by the sword and lived.
15 He was granted power to give breath to the image of the beast, that the image of the beast should both speak and cause as many as would not worship the image of the beast to be killed.
16 He causes all, both small and great, rich and poor, free and slave, to receive a mark on their right hand or on their foreheads,
17 and that no one may buy or sell except one who has the mark or the name of the beast, or the number of his name.
18 Here is wisdom. Let him who has understanding calculate the number of the beast, for it is the number of a man: His number is 666.
Rev 13:1-18 (NKJV)