The Greek verb epaischunomai (ἐπαισχύνομαι) means to be ashamed of or to feel shame about. It appears 11 times in the New Testament and is theologically decisive: Paul and other writers invoke it to address the temptation to be ashamed of the Gospel in a culture that viewed crucifixion as ultimate shame.
Romans 1:16 is Paul's foundational declaration: "For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation." The cross was a stumbling block and foolishness to the Roman world — ultimate shame. Paul's response is the total inversion of that shame: what the world considers shameful is the power and wisdom of God. Mark 8:38 warns: "Whosoever therefore shall be ashamed of me and of my words... of him also shall the Son of man be ashamed."