This same conversation and challenge is also recorded in Matthew 16:24 and Mark 8:34, except that only Luke included the term "daily." Except for one brief reference in Matthew 10:38, this conversation marks the first explicit reference in the Bible to the practice of crucifixion, and it apparently assumes that the disciples were already well aware of this typically Roman method of execution.
"Taking up the cross" referred to the usual requirement that each condemned man haul his own cross to the place of execution. Jesus knew that He would soon have to be doing this Himself (John 19:16-17).
Christians sometimes use this phrase without appreciation of its true meaning, thinking of some burden (such as sickness or poverty) as "the cross" they must bear. Such things can be serious problems, of course, but they are not instruments of execution, such as a cross. In effect, the Lord was telling His disciples that following Him must mean nothing less than a daily willingness to die for Him, if need be. As Paul would say: "I am crucified with Christ" (Galatians 2:20); "I die daily" (1 Corinthians 15:31).
Many disciples have, indeed, suffered martyrdom for Christ's sake, but all should at least be willing to deny themselves each day. "Taking up the cross" does not necessarily mean dying as Christ did, but it does mean consciously dying each day to the world and living unto Him. For "they that are Christ's have crucified the flesh with the affections and lusts" (Galatians 5:24), and they gladly affirm this testimony: "God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world" (Galatians 6:14). HMM http://www.icr.org/articles/type/6/