What Happened?
Jesus, after his last Passover, takes his disciples to Gethsemane to await his arrest (Matthew 26:30, Mark 14:26). Judas, shortly after midnight, arrives in the garden with a mob to take him. After a brief confrontation, which leads to Peter cutting off a servant's ear, the eleven disciples run from the garden in fear (John 18:1 - 12). Mark then reveals a startling interaction which caused an unnamed man to flee nude away from Jesus and those arresting him.
Now a certain young man was following Him (Jesus), having a linen cloth wrapped around his naked body; and the young men (likely Roman soldiers) seized him, but he escaped, leaving the linen cloth behind, and ran from them naked (Mark 14:51 - 52, HBFV throughout).
Why Include It?
On the surface, it is unclear why Mark felt the above event deserved to be mentioned. The addition of such a seemingly unimportant fact, during the arrest of Jesus, adds nothing to his overall narrative and changes nothing about the course of events he recorded.
The gospels of Matthew and John don't mention the incident of Mark 14:51 - 52 since they had fled and didn't see it take place. Luke also does not mention a naked young man fleeing Jesus' arrest. Although he thoroughly investigated both written and eyewitness testimonies of Jesus' ministry (Luke 1:1 - 4), it is possible he did not record it as no one told him about it.
Mark wrote his gospel seventeen years before Luke penned his. Some commentaries believe that Luke had access to it as part of his research. If this were the case, he clearly thought the event in question did not need to be included in his own work.
Guessing Game
Mark offers no hint as to the identity of the young man who fled naked away from Gethsemane. The man is clearly not one of Jesus' disciples as they had already run away (Mark 14:50). Biblical commentaries offer a wide range of conjectures as to who this mysterious person might be.
One Bible commentary on Mark 14:51 - 52 thinks the young man could have been the owner of Gethsemane (Barnes' Notes on the Bible) or someone who lived in a house in the garden (John Gill's Exposition of Bible).
Other commentaries speculate the fleeing young person was an unknown man who woke up and went to investigate the noise (Adam Clarke's Commentary, John Wesley Explanatory Notes, Johnson's Notes on the New Testament). At least one commentary thinks the man may have been Lazarus (Bullinger's Companion Bible Notes).
Some commentaries, however, do support the belief that the fleeing young man from Jesus was Mark (Bible Illustrator, Expositions of Holy Scriptures).
Did He Live Near Gethsemane?
The first mention of Mark, by name, in the New Testament is in Acts 12. Peter, after being miraculously released from a Jerusalem prison, walked to a house owned by Mark's mother Mary.
And as he (Peter) was pondering this, he came to the house of Mary, the mother of John who was surnamed Mark, where many were gathered together and were praying (Acts 12:12).
Mary was a prominent woman in the early church at a time of persecution. She was financially prosperous enough to own a home in Jerusalem large enough to host a house church.
Mark lived with his mother in Jerusalem, as shown by him going with Paul and Barnabas from the city to Syrian Antioch (Acts 11:26, 29 - 30, 12:25). He had quick access to the Garden of Gethsemane as it was a short distance from Jerusalem's walls.
Was It Him?
Mark, as a young man, lived in Jerusalem. He could have visited Gethsemane, where Jesus was arrested, at any time. Although he does not record his own name as the man who fled Jesus, this was not uncommon.
Most of the New Testament writers seldom, if ever, mentioned themselves in their writings. Matthew, for example, only records his name twice in his gospel while Luke doesn't mention himself by name in his gospel or in the book of Acts!
While admittedly not conclusive, it is highly likely the young man who fled naked from Jesus was Mark. If this is the case, he probably included it in his gospel simply because he was involved. This would explain why he was the only one to record the incident.
One Bible commentary summed up the identity of who was led to flee naked from Jesus and his arrest as follows.
"Probably this young man was Mark. Only he tells the incident, which has no bearing on the course of events, and was of no importance but to the person concerned." (Expositions of Holy Scriptures by MacLaren).