It doesn't explain it at all.
Sure to explain this you'd have to either:
Claim that the author or Mark had access to Matthew 5-7 and Luke 9:51-18:14 but for some reason chose to ignore them - perhaps because of a major schism in the early church as to the importance of the Lord's Prayer. Or.
The early versions of Matthew and Luke that the author or Mark had access to did not include these sections and they are later interpolations. We, of course, have no idea what was in the earliest versions of the gospels as the earliest fragments we have are from 100 years after their purported writing - in the case of most of the content several hundreds of years later.
I think Mark did have access to those sections of Matthew and Luke. As Riley says, the Sermon on the Mount (Mt 5-7) is placed where it is in order to show how the part of Isaiah's prophecy concerning 'Galilee of the Gentiles' - "the people living in darkness have seen a great light" (Mt 4:16) - is fulfilled through Jesus' teaching (Riley, The First Gospel, p.24,72). So it must have been part of Matthew's original book.
Luke says in Acts 1:1 that in his first book he wrote about "all that Jesus began both to do and to teach, until the day that he was taken up." Luke appears to have divided his Gospel into three, concentrating first on "all that Jesus began to do" and then on "all that Jesus began to teach", then on the events culminating with "the day that he was taken up".
"At Luke 9:51 Luke begins the next main division of his Gospel, in which he sets out more fully the teaching of Jesus" (Riley, Preface to Luke, p.56).
"As the day of His ascension approached, Jesus resolutely set out for Jerusalem." (Note the reference in Acts 1:1 and Luke 9:51 to Jesus' ascension).
The reason I thought Mark did not lift the Lord's Prayer out from either of these sections is that when you read Matthew's and Luke's contexts, the prayer seems no more or less important than what is said in those contexts.
As to Mark's main purpose: "... it is clear that Mark has selected his material on a definite plan. While there is inevitably an element of Jesus' teaching involved in speaking of his activities (and Mark frequently refers to Jesus as Teacher and to his activity in teaching) and an element of narrative involved in setting out what Jesus taught, there is a broad distinction between the proclamation of what Jesus did and the exposition of his teaching. Mark has concentrated on the former. His book is strictly kerygmatic: its purpose is to call men to "repent, and believe the gospel" (1:15). It is a book of appeal to Christian commitment, the consequences of which could be worked out in the continuing life in the church. That was a limited purpose but a noble one, fitting for what we may deduce to have been Mark's own ministry from the references to him in the New Testament. (Riley, The Making of Mark, p.214).