President Johnson had stated that two American destroyers (a type of warship), the U.S.S. Maddox and the U.S.S. C. Turner Joy, had been attacked without provocation in international waters. He then asked the Congress for permission to accelerate American involvement in Vietnam and to bomb certain sites within North Vietnam. Congress gave him permission with the Gulf of Tonkin Resolution.
The Pentagon Papers, a series of articles being published in the New York Times, revealed this to be, at best, an exeration of the truth. It suggested that the American destroyers might even have penetrated into North Vietnamese territorial waters prior to the attack on them. This intrusion would have justified, under international law and international precedent, a retaliation by North Vietnam. This retaliation is what Johnson described at an unprovoked attack (an apparent lie).
These papers were being published during the Nixon administration which tried to stop their continued publication. The Supreme Court ruled that this would amount to "prior restraint" and is not allowed. They were published in their entirety.
In the most stunning of displays, the Pentagon Papers and the President's desire to block their publication proves a fundamental saying regarding President Nixon's administration. The issue that seems to have plagued Nixon throughout his tenure was "what did the President know and when did he know it." There had always been the belief that the office of the President was committed to not making mistakes and doing what was in the best interests of the nation without fail. Yet, when the Pentagon Papers were released and when Nixon sought an injunction to block their publication it ended up proving that the President might have consciously understood the dangers of the paths being pursued. The Court's ruling against this injunction showed to a great extent how the office of the President had lost its Constitutional way and how recalibration was a must. The papers showed the brutal level of miscalculation and error being committed and the desire to only examine political fall out from such decision, and little else. Haldeman's quote about how the papers alter the perception of the President doing wrong looms very large in such a context.
The Supreme Court ruled that the Nixon Administration could not block the publication of the Pentagon Papers.
The papers showed basically that the government had not been telling the truth about what was going on in the Vietnam War. The papers covered the time period up to 1965 and so they included the time around the Gulf of Tonkin Resolution. They showed that the government had not told the full story of the Gulf of Tonkin Incident and they showed that LBJ had been telling the people no combat troops would be sent even as he planned to send them.
The papers really contributed to the "credibility gap" that made the public distrust the government.