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.