What was the significance of the "smoking gun" recording of Nixon?
The significance of the "smoking gun" tape is that it made completely clear that Pres. Nixon had entered into a criminal conspiracy that was meant to obstruct justice. This made it inevitable that Nixon would have to resign or be impeached.
Throughout the Watergate scandal, Nixon had argued that he never tried to cover up the actions of his subordinates. He reluctantly released tapes that he said proved this. However, he was forced (after the Supreme Court ruled against him in US v. Nixon) to hand over all of the tapes that the Justice Department wanted. Among these was this tape that clearly showed him ordering aides to try to get the FBI to shut down their investigation.
Once this tape was made public, Nixon's fate was sealed, which is why the tape is significant.