Many readers of The Bible are somewhat puzzled when they come across the above verses. Satan said that the kingdoms of the earth were his to give, and more surprisingly, Jesus Christ didn't refute that claim.
Satan's World, For A Little While Longer
When Lucifer (see Did God Create The Devil?) rebelled, he was defeated and cast down from the heavens back to the earth: "How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground" (Isaiah 14:12 KJV).
Jesus Christ also described the fall, as He witnessed it in His pre-human form (see The Logos): "I saw Satan fall like lightning from heaven." (Luke 10:18 RSV).
Although he may not be absolutely confined to earth (e.g. Job 1:6), the earth is where Satan now resides and has his throne -
What Satan Fears Most - The Return of Jesus Christ
Satan has already been defeated; he just hasn't been removed yet (see The Lame Duck). The Return Of Jesus Christ will mark the end of Satan's rule and influence on earth. He will soon get all that's coming to him, and he knows it.
"But woe to you, O earth and sea, for the devil has come down to you in great wrath, because he knows that his time is short!" (Revelation 12:12 RSV)
"Then I saw an angel coming down from heaven, holding in his hand the key of the bottomless pit and a great chain. And he seized the dragon, that ancient serpent, who is the Devil and Satan, and bound him for a thousand years, and threw him into the pit, and shut it and sealed it over him, that he should deceive the nations no more, till the thousand years were ended. After that he must be loosed for a little while. Then I saw thrones, and seated on them were those to whom judgment was committed. Also I saw the souls of those who had been beheaded for their testimony to Jesus and for the word of God, and who had not worshiped the beast or its image and had not received its mark on their foreheads or their hands. They came to life, and reigned with Christ a thousand years [see The Last Day]. The rest of the dead did not come to life until the thousand years were ended. This is the first resurrection. Blessed and holy is he who shares in the first resurrection! Over such the second death has no power, but they shall be priests of God and of Christ, and they shall reign with Him a thousand years." (Revelation 20:1-6 RSV)
"And when the thousand years are ended, Satan will be loosed from his prison and will come out to deceive the nations [see Could Satan Repent?] which are at the four corners of the earth, that is, Gog and Magog, to gather them for battle; their number is like the sand of the sea. And they marched up over the broad earth and surrounded the camp of the saints and the beloved city; but fire came down from heaven and consumed them, and the devil who had deceived them was thrown into the lake of fire and sulphur where the beast and the false prophet were, and they will be tormented day and night for ever and ever." (Revelation 20:7-10 RSV)
Fact Finder: Will God soon crush Satan?