The allegation was that Ted Kennedy, through another Senator, made contact with the Soviet Union because he wanted to stop Reagan being re-elected as he felt his foreign policy stands against he Soviet Union meant nuclear war was likely. The alleged letters stated,
If the proposal is recognized as worthy, then Kennedy and his friends will bring about suitable steps to have representatives of the largest television companies in the USA contact Y. V. Andropov for an invitation to Moscow for the interview. Specifically, the board of directors of ABC, Elton Raul and the television columnists Walter Cronkite or Barbara Walters could visit Moscow. The senator underlined the importance that this initiative should be seen as coming from the American side.The full memo can be read here. According to Free Republic the memo was found in the Soviet Archives by a Times reporter after the KGB files were opened.
Interestingly, the authenticity of the letter/memo has never actually been clarified that I have seen. There is the obvious reaction that it is merely a "Zinoviev Letter" designed to smear Kennedy. Although I'm not quite sure what (a) the purpose of smearing him in 2006 would have been, and (b) he was already a "Marmite" politician anyway given the infamous Chappaquiddick Incident.