Confronted by Samuel with his sinful disobedience to the Lord's command to "utterly destroy" the Amalekites, King Saul offers "reputable repentance" in response. Saul is more concerned with saving face with the leaders of Israel and his people than he is with recognizing the seriousness of what his disobedience has done to God's reputation, as well as his own relationship with the Lord.
Saul says, "I have sinned, yet honor me." Saul wants a repentance that allows him to admit he's done a bad thing, yet believes he can still worship God without a genuine turning from his sin. Sadly, we hold to the same error, believing we can continue our sinning ways through the week while singing God's praise on Sunday with no real conviction or repentance.