I've heard preachers say that "repentance" is a military term which means "about-face", but I've searched the Greek word, μετανοέω, in my lexicons none discuss this being a military term. Also, I have a number of commentaries, yet the only one I can find that says it is a military term is The Teacher's Commentary, which I've never heard of and I don't even know what I purchased to get it in my library. I've copied the section below, but it doesn't say much about it.
"Repentance and faith. The word repent is a military term meaning make an about-face. The men to whom Peter spoke had refused to accept Jesus as Lord and Messiah. They had hesitated, then passively participated in His execution. Now they were asked to make a clear-cut commitment and symbolize their response of faith by public baptism. And if they did? Then everything that Jesus’ death and resurrection promised would become theirs: full forgiveness of sins and the gift of the Holy Spirit. The God they had scorned would welcome even them and, entering their lives, fill them with power to launch out new lives."
Larry Richards and Lawrence O. Richards, The Teacher’s Commentary (Wheaton, IL: Victor Books, 1987), 767.