At the meal, John describes the disciple whom Jesus loved as reclining close to Jesus. Peter signals to him, and the disciple leans back toward Jesus to ask who the betrayer is.
The scene is difficult to visualize if everyone is imagined sitting upright in modern chairs.
At formal meals, diners could recline on couches or cushions, typically leaning on the left side while eating with the right hand. A guest immediately in front of another could be described as reclining near that person's chest or bosom and could lean back to speak quietly. This arrangement explains both the beloved disciple's proximity to Jesus and Peter's use of a signal rather than loudly asking across a modern-style table.
The Gospel itself does not name the beloved disciple in this passage.
The meal custom turns an apparently awkward phrase into a natural description of seating.
It also gives the scene intimacy: the disciple positioned nearest Jesus can quietly ask the question that troubles the group, while the others remain unaware of the full exchange.