The song is a dark character sketch featuring a soft, haunting trumpet played by Randy Brecker, piano backing from E Street Band member Roy Bittan and upright bass from jazz veteran Richard Davis. Brecker's jazz-inspired horn part adds poignancy to the song and suggests a film noir feel. The lyrical, understated tune forms a bridge between the powerful "She's the One" and the album's epic finale "Jungleland". It also forms a bridge between the New Jersey-based songs throughout the Born to Run album and the New York City setting of "Jungleland". Presumably, the hoods in "Meeting Across the River" are heading over the Hudson River from New Jersey to New York to meet their connection.
The lyrics describe a low-level criminal, down on his luck but with one last chance at success for him and his friend, Eddie, that involves meeting a man across the river. Springsteen portrays his characters sympathetically. The narrator appears to be desperate; he needs to borrow some money and a ride from Eddie, and his girlfriend is threatening to leave because he has pawned her radio. The details are vague, but the consequences if they fail at their task seem to be very serious, and the song's sombre tone does not imply that they will succeed. Lyrics also imply that the man has never really been qualified for crime; however, the promise of a big payoff, and the thought that this might make his girlfriend stay with him, has caused him to get in over his head. Original pressings of Born to Run billed the song as "The Heist", suggesting what the man across the river was employing the narrator and Eddie for. In some ways similar in theme to The Velvet Underground's "Waiting for the Man", "Meeting Across the River" has less urgency but is a more detailed depiction of a drug deal.
The song is often paired with "Jungleland" in concert, though without the Randy Brecker trumpet part from the record and with regular bass guitarist Garry Tallent.