The guy on the plane is the one who sits next to Rachel as she races across the Atlantic to tell Ross she loves him on his wedding day. He gets annoyed by Rachel tapping her hands on her lap and tries to ignore her by putting on headphones.
Later on, as Rachel is telling her sob story to another passenger, he takes off his headphones and interrupts her. The guy isn't very sympathetic to Rachel's rationalizations for why she's going to confess her love to Ross at his wedding to another woman. He tells her that she's a "horrible person", that if she really loved Ross she wouldn't be trying to stop his wedding, and that no good will come from her doing it. Rachel refuses to listen to him and remains convinced she's in the right.
The man then starts to ignore her, but not before telling her, "...it seems to be perfectly clear, that you WERE on a break."
In the closing credits of the episode, Hugh Laurie is mistakenly credited as "The Gentleman on the Phone" instead of "The Gentleman on the Plane."