This refers not to problems believers face, but to death itself. (Utley, R. J. D. (2004). Vol. Volume 3A: The Gospel According to Luke. Study Guide Commentary Series. Marshall, Texas: Bible Lessons International.)
When the Roman Empire crucified a criminal or captive, the victim was often forced to carry his cross part of the way to the crucifixion site. Carrying his cross through the heart of the city was supposed to be a tacit admission that the Roman Empire was correct in the sentence of death imposed on him, an admission that Rome was right and he was wrong. So when Jesus enjoined His followers to carry their crosses and follow Him, He was referring to a public display before others that Jesus was right and that the disciples were following Him even to their deaths. (Walvoord, J. F., Zuck, R. B., & Dallas Theological Seminary. (1983-). The Bible knowledge commentary : An exposition of the scriptures. Wheaton, IL: Victor Books.)Luke 14:28–30 Discipleship requires planning.
Discipleship requires a conscious advance commitment, made with a realistic estimate of the ultimate personal cost. The practical nature of the circumstances Jesus so vividly pictures underlines the fact that Christian discipleship is not some theoretical abstract ideal but hard reality. (Gaebelein, F. E., Carson, D. A., Wessel, W. W., & Liefeld, W. L. (1984). The Expositor's Bible Commentary, Volume 8: Matthew, Mark, Luke. Grand Rapids, MI: Zondervan Publishing House.)Luke 14:31–33 Discipleship requires sacrifice. We must give up everything for Jesus.
Yielding up the right of ownership, rather than outright disposal of them. The disciple of Jesus may be given the use of things in trust, as a stewardship, but they are no longer his own. (Ibid.)Nothing we own is more valuable than being a disciple of Jesus.