Vladimir Neski was a liberal Democrat and an outspoken opponent of the oil privatization in post-soviet Russia. When Yuri Gretkov and Ward Abbott stole $20 million from the CIA to invest in the Russian oil business, Neski was in their way.
Bourne's first mission, albeit unofficially, was carried out at Brecker Hotel in Berlin, where he should kill Neski. Since surprisingly his wife was staying with him, Bourne made it look like she killed her husband and then killed herself. The assassination was never mentioned in Bourne's files. Thus everyone except Conklin (and most likely Abbott) believed Bourne's first mission to be in Geneva.
Documents regarding the theft of $20 million black money from the CIA and the murder of Neski are later called "The Neski Files".
The Bourne Supremacy
In The Bourne Supremacy, Bourne eavesdrops Pamela Landy telling an asset in Naples airport that Bourne killed two intelligence officers, one of them a highly trained field officer, in Berlin. Despite not doing this, it brings him back memories of the Neski mission. Bourne then searches the Web for news articles about the killings and finds Brecker Hotel.
Bourne later visits the Neskis' daughter Irena Neski in Moscow, Russia to apologize and tell her that her mother was not the murderer and that he was.