he who overcomes
See Who is the Overcomer?
keeps my works
Jesus spoke of the need for endurance, especially as lawlessness would abound and the love of many grew cold (Mtt. Mat. 24:12-13). There are many distractions which can undermine fruitful and consistent development in the Christian life. In the parable of the four soils, Jesus explained that the devil is partly to blame, but that some lacking any root will fall away due to temptation. Still others have their potential works choked by the cares, riches, and pleasures of life. But those who have a noble and good heart hear the word and bear fruit with patience (Luke Luke 8:11-15).
Keeping His works requires abiding (μενω [menō] ) in His word (John John 8:31-32). To abide is to live, dwell, lodge . . . [and is used] of someone who does not leave the realm or sphere in which he finds himself1 . Thus, we are to be immersed and live in His Word. Otherwise we will not be His disciples and whatever we keep wont be His works.
until the end
For the believer, the end arrives when either we step through the doorway from this life into the presence of God (2Cor. 2Cor. 5:8) or we remain alive until the coming of the Lord (John John 14:3; 1Th. 1Th. 4:15).
power is εξουσίαν [exousian] : The power exercised by rulers or others in high position by virtue of their office.3 This authority is not innately the overcomers, but is granted to him by virtue of his identity with Christ, for it is Christ who is destined to rule all nations with a rod of iron (Rev. Rev. 12:5+; Rev. 19:15+). The overcomer will reign with Him a thousand years (Rev. Rev. 20:6+).
1 Frederick William Danker and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago, IL: University of Chicago Press, 2000), s.v. meno.
2 Rabbinic interpretation associated the title Shiloh with the Messiah: a midrash takes Shiloh to refer to King Messiah (Genesis R. 98.13), the Babylonian Talmud lists Shiloh as one of the names of the Messiah (Sanhedrin 98b), and Medieval Jewish Biblical expositor Rashi makes the following comment: Shiloh - i.e. King Messiah whose is the Kingdom. Note that Eze. Eze. 21:25-27 was given to Zedekiah, the last king of the Davidic dynasty. Shiloh means to he whose it is or to he who it belongs or he whose right it is or to whom kingship belongs (Midrash Rabbah 98).
3 Danker, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, s.v. exousian.