In Spectre, Bond is in a place named "l’américain", the hotel where Mr. White spent his vacation. Bond found in this place a record with the label "Vesper". Maybe Mr. White wanted to kill Vesper? What is the purpose of this scene?
The hotel room is where Mr. White used to try and track Oberhauser. The tape he finds says "Vesper Lynd - Interrogation".
If you remember back to Casino Royale, Bond at one point is kidnapped and tortured by Le Chiffre.
Mr. White intervenes and despite Le Chiffre's pleas for mercy, executes him. As we find out later in the film, Vesper Lynd was a double agent - she made a deal with Mr White (and his organisation, Quantum) to spare Bond's life, in exchange for the $120 million.
The tape Bond finds at the hotel is some interrogation between Mr. White and Vesper where this deal was likely concluded.