Much like today's political climate, the United States was involved in a confusing war that had been going on far too long, and there were differences on how to move forward (or backwards).
In this case, the DNC in Chicago endorsed President Lyndon Johnson's administration's platform on the war in Vietnam and chose VP Hubert Humphrey as the party's nominee for president. Humphrey had adopted Johnson's views of staying in the war awaiting the results of the Paris Peace Talks, where the leaders of both North and South Vietnam would meat in Paris to negotiate peace.
Johnson had opted not to seek re-election because he wanted to concentrate on peacemaking. It's very rare that a President does not run for a second term, but it has happened... see the notes at the bottom for other occurrences.
Many Democrats had hoped that Eugene McCarthy, who called for an immediate withdrawal from Vietnam, would be the nominee.
The decision to support Vice President Humphrey and in turn Johnson's platform on the Vietnam War resulted in a heated three-hour debate inside the convention hall.
Meanwhile, a full-scale riot erupted outside in the streets, where antiwar protesters fought with police and the National Guard. By the end of the convention, some 668 demonstrators had been arrested.
Eight of the protesters were charged with conspiracy in connection with the violence. They were known collectively as the "Chicago Eight". But one of the eight was tried separately after declaring a mistrial and they were renamed the "Chicago Seven".
Needless to say, America was shocked by the images of armed conflict in the streets broadcast on TV and in the papers. The Republican Party quickly reacted and vowed to restore law and order, earning Richard Nixon a lot of support and eventually the Presidency.
Other Presidents not seeking re-election:
Lyndon Johnson, opted to withdraw from the 1968 election to concentrate on peacemaking, though his Vietnam War policy did not support this.
James Polk -- retired after one term and did not seek re-election
And James Buchanan's party did not nominate him for re-election in 1860... he was a lame duck who didn't do much to stop the Civil War and is rated as one of the worst Presidents in history.
For more information about this year's Democratic National Convention visit their website:
Here's more about the riots from the Chicago History Museum: http://www.chicagohs.org/history/politics/1968.html
and I can't believe people are encouraging another riot...