Bork was the acting Attorney General in the Nixon administration who carried out the infamous "Saturday Night Massacre" in which Watergate Special Prosecutor Archibald Cox was fired. The Attorney General and Deputy Attorney General had resigned rather than carry out Nixon's orders to fire the prosecutor.
At the time of Bork's nomination there were many Republican senators who were adamantly opposed to having Bork on the court -- mainly because his role in the Watergate affair indicated a lack of principle, an excess of political ambition, or both.