The following commentary is excerpted from the Navarre Bible Commentary on the Transfiguration of Our Lord:
2-10. We contemplate in awe this manifestation of the glory of the Son of God to three of His disciples. Ever since the Incarnation, the divinity of our Lord has usually been hidden behind His humanity. But Christ wishes to show, to these favorite disciples, who will later be pillars of the Church, the splendor of His divine glory, in order to encourage them to follow the difficult way that lies ahead, fixing their gaze on the happy goal which is awaiting them at the end. This is why, as St. Thomas comments (cf. "Summa Theologia", III, q. 45, a. 1), it was appropriate for Him to give them an insight into His glory. The fact that the Transfiguration comes immediately after the first announcement of His passion, and His prophetic words about how His followers would also have to carry His cross, shows us that "through many tribulations we must enter the kingdom of God" (Acts 14:22).
What happened at the Transfiguration? To understand this miraculous event in Christ's life, we must remember that in order to redeem us by His passion and death our Lord freely renounced divine glory and became man, assuming flesh which was capable of suffering and which was not glorious, becoming like us in every way except sin (cf. Hebrew 4:15). In the Transfiguration, Jesus Christ willed that the glory which was His as God and which His soul had from the moment of the Incarnation, should miraculously become present in His body. "We should learn from Jesus' attitude in these trials. During His life on earth He did not even want the glory that belong to Him. Though He had the right to be treated as God, He took the form of a servant, a slave (cf. Philippians 2:6)" (St. J. Escriva, "Christ Is Passing By", 62). Bearing in mind WHO became man (the divinity of the person and the glory of His soul), it was appropriate for His body to be glorious; given the PURPOSE of His Incarnation, it was not appropriate, usually, for His glory to be evident. Christ shows His glory in the Transfiguration in order to move us to desire the divine glory which will be given us so that, having this hope, we too can understand "that the sufferings of this present time are not worth comparing with the glory that is to be revealed to us" (Romans 8:18).