Revelation 7:1 And after these things I saw four angels standing on the four corners of the earth, holding the four winds of the earth, that the wind should not blow on the earth, nor on the sea, nor on any tree.
Revelation 7:2 And I saw another angel ascending from the east, having the seal of the living God: and he cried with a loud voice to the four angels, to whom it was given to hurt the earth and the sea,
Revelation 7:3 Saying, Hurt not the earth, neither the sea, nor the trees, till we have sealed the servants of our God in their foreheads.
Revelation 3:7 And to the angel of the church in Philadelphia write; These things saith he that is holy, he that is true, he that hath the key of David, he that openeth, and no man shutteth; and shutteth, and no man openeth;
Revelation 3:10 Because thou hast kept the word of my patience, I also will keep thee from the hour of temptation, which shall come upon all the world, to try them that dwell upon the earth.
"Will Keep": τηρέω tēréō, tay-reh'-o; from τερός terós (a watch; perhaps akin to G2334); to guard (from loss or injury, properly, by keeping the eye upon)
To understand the "mark of the beast", it is important to get some references to similar markings or "seals" placed on others where the Bible gives a bit more detail. From Revelations chapter 7, we see that the angels commanded by God to start the tribulation and hurt the earth were told to stop and wait until "we have sealed the servants of our God in their foreheads". As was stated before in this thread by another, forehead represents our mind. So for the Christians to be sealed in their minds, they need to have the knowledge of what is going to happen or at least God attempted to give them the knowledge and they rejected it for traditions of man. This was spoken of by Jesus Christ,
Matthew 24:14 And this gospel of the kingdom shall be preached in all the world for a witness unto all nations; and then shall the end come. I do want to just ensure you understand the Greek meaning to the "too keep" in Revelations chapter three, this verse does not support a rapture, God will not prevent Christians from experiencing the tribulation as we will be here. The word means "to watch" and "to Guard", which is done by giving us the knowledge of what will happen so we are not deceived.
Revelations 13:15 And he had power to give life unto the image of the beast, that the image of the beast should both speak, and cause that as many as would not worship the image of the beast should be killed.
Revelations 13:16 And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads:
Revelations 13:17 And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name.
Now let us break down the "mark of the beast", we learn three things here that are worth your attention. The first is that those that "would not worship the image of the beast should be killed", so we understand this is about being deceived by the anti-Christ to believe he is Jesus Christ to the point we "worship" him. Second we learn that no one can live or exist in a functioning way as we can not "buy or sell (food, water, shelter, etc)" without some kind of "mark" of the beast, showing that we are his followers and worshippers. The devil will come down pretending to be Jesus which is why he is called the anti-Christ, as such he will be copying the known parts of Jesus return such as the kingdom on Earth Jesus will have. So when you hear the term "beast", it is just meaning "satan's government", "Babylon" is meaning "satan's kingdom". The third thing we learn is that the "mark of the beast" will be in their foreheads or on their hand, like I pointed out before someone already said this, but the forehead as we talked about in regards to Christians and the seal was belief or knowledge. Those that are marked on their foreheads believe satan is Jesus, and are truly worshipping him as their god. Now the mark on the hand is action, example would be "right hand of God" to speak of God's servants doing his bidding, so those with the mark on their hands are those working for satan by converting people into believing he is Jesus. Both of these are spoken about by Jesus himself:
Matthew 24:10 And then shall many be offended, and shall betray one another, and shall hate one another.
Matthew 24:11 And many false prophets shall rise, and shall deceive many.
Matthew 24:12 And because iniquity shall abound, the love of many shall wax cold.
Matthew 24:13 But he that shall endure unto the end, the same shall be saved.
Matthew 24:23 Then if any man shall say unto you, Lo, here is Christ, or there; believe it not.
Most of the world even many Christians will "betray one another", by convincing them or trying to convince them into believing "here is Christ". "Love" between men will grow "cold", because those that will be deceived by satan will "hate" those that do not believe to the point they will report them to satan and his demons by saying things like "Lord! My neighbor Robert does not believe you are Jesus!" Then the demons will take them and bring them to jail, maybe kill them. As Jesus said:
Matthew 24:9 Then shall they deliver you up to be afflicted, and shall kill you: and ye shall be hated of all nations for my name's sake. The reason why satan can not just use his supernatural power to know who the Christians are is the "seal" of God, one of the rules God gives to satan before he comes down is that each person has to expose themselves or be exposed by another. Which is why Jesus gives us the knowledge to get through the tribulation the easies way: Matthew 24:16 Then let them which be in Judaea flee into the mountains: 17 Let him which is on the housetop not come down to take any thing out of his house: Hide, don't draw attention to yourself, don't talk to anyone, and NEVER try and speak out against the anti-Christ. Works and Faith are gone at this point, satan will be here with all the demons in their spiritual bodies exposing the truth to everyone that the Bible was right. Our only command from God during this time is to endure it, and not allow ourselves to be deceived or sin against God wilfully (the unforgivable sins of blasphemy against the Holy Spirit and willfully sinning after knowing the whole truth is during the tribulation. If you are called to be part of the "two witnesses" you need to say and do what the Holy Spirit says or your soul will be killed in the Lake of Fire, you can not knowingly and willingly sin at this time either your soul will also be killed in the Lake of Fire).
Revelation 13:18 Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.
Revelation 14:9 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand,
Revelation 14:10 The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
If you can't go run and hide in a cave in some wilderness during the Tribulation, the Father is so amazing he gives us another way to endure the end. "Here is wisdom. Let him that hath understand count the number of the beast: for it is the number of a man;" God is poking you in the head right now saying, "Hey! You! Listen to this, if you have understanding!" In Chapter 14 when John speaks of satan's kingdom ending and the wrath of God, he says "if any many worship the beast and his image, and recieve his mark in his forehead, or in his hand, The same shall drink the wine of the wrath of God". Wait...the "wisdom" is to "count the number of the beast", but those that have the number of the beast will not receive God's wrath..how is that?!? Simple, "it is the number of a man", meaning we all have it. Are we in Jesus' kingdom now? No. Do we have rulers now? Yes. Do we obey our rules now, so we can exist in our countries without going to jail or be killed? Yes. The point is; just as we are in a "kingdom" now as citizens of USA, France, Russia, Egypt. We will also be citizens of satan's kingdom during the tribulation, as he is going to rule the entire world. As we do not rebel and attack our country/law enforcement/leaders now, we should not when satan is king either. The best way I have found to explain the "number of the beast" is your social security number we have now, it shows that we are citizens of the USA and that is all. The best way to live in satan's kingdom is exactly what your HR department tells you when you start a new job, "no talking about religion, politics, or sex". As long as you are not told to sin against God or help satan deceive others, fake it until you make it.