What does Mark 14:51 mean?"Linen cloth" is sindon, originally from an unknown language. It is a fine cloth used as a loose robe or to wrap the dead.
The Scriptures never say who this young man is, but scholars postulate it is Mark, himself. John-Mark is the cousin of Barnabas, Paul's evangelism partner. He travels with Paul and Barnabas on their first missionary journey (Acts 13:5) but abandons them partway through (Acts 15:37–38). Paul refuses to take him on their next trip, but Barnabas wishes to give his cousin a second chance. So Paul and Barnabas split up, and Barnabas takes Mark (Acts 15:39–41). This makes sense, since "Barnabas" means "son of encouragement" (Acts 4:36). Sometime later, Mark and Paul are reconciled (Philemon 1:24; 2 Timothy 4:11).
If the young man is Mark, it's not clear why he is here. As far as we can tell, Jesus celebrated Passover only with the twelve disciples (Mark 14:17), and they followed Him to Gethsemane (Mark 14:32). But tens of thousands of travelers have come to Jerusalem for the Passover, and it's reasonable to assume many have camped on the Mount of Olives. It's possible Mark's family is camped nearby and he's come to see what is going on, clad only in the thin blanket he was sleeping in.
Some have suggested the boy lives in the home in which Jesus and the disciples celebrated the Passover. This is possible. Mark's mother apparently lived in Jerusalem. In Acts 12:1–5, Herod Agrippa imprisons Peter during the Feast of Unleavened Bread, which is held in Jerusalem. After angels help Peter escape, Peter runs to Mark's mother's home (Acts 12:12).
But all this is speculation; Scripture doesn't explicitly tell us who this young man is. Only these two verses mention this incident.