They did not understand. But they got the bit about the power!
"After leaving the mountain..." The text refers to the Transfiguration. This story is omitted in the Lectionary at this time. It has its turn every year in Lent. Also the Lectionary omits the cure of the epileptic whom the apostles were unable to cure.
Jesus and his team are journeying through Galilee. He does this in secret, "he did not want anyone to know." He teaches for the third time that "the Son of Man will be delivered into the hands of men: they will put him to death; and three days after he has been put to death, he will rise again." Again they don't understand. They are afraid to ask him!
This is the centre for the Galilean ministry of Jesus. It seems it was the house of Peter by the lake. They are inside the house when Jesus asks them what they were talking about on the road. "They said nothing because they had been arguing about which of them was the greatest." I often wonder if their answer was the word "nothing" as a child would answer, or were they really silent.
Jesus gives them a lesson on service. "If anyone wants to be first, he must make himself last of all and servant of all." Jesus puts his arms around a little child and said to them, "anyone who welcomes one of these little children in my name, welcomes me, and anyone who welcomes me, welcomes not me but the one who sent me."
This is the lesson on greatness in the kingdom. Remember the mother of James and John asking questions about positions of greatness. Remember Jesus washing Peter's feet. it is a hard lesson. it is easy to overlook it.
The kingdom is about humiliation and suffering. It is not a glory trip. It is about service to others. It is very serious teaching.