In 1968, because of controversy over the Vietnam War, LBJ decided not to run again, so there was a nomination fight. Unlike nowadays, where most of the delegates are picked in primaries, back then, most of the delegates were picked by the state party leadership.
The big controversy among the Democratic party in 1968 was over the war. The “front runner” was Hubert Humprey, LBJ’s vice president, who’s position on the war was similar to that of LBJ’s (work out a negotated peace, based on the peace talks going on in Paris and withdraw). However, a lot of Democrats, especially younger Democrats who were at risk of being drafted, were more strongly antiwar, and supported an immediate withdrawal from Vietnam, and the anti-war democrats lined up behind, first, Bobby Kennedy, and then after he was assassinated, Eugene McCarthy, a senator from Minnesota, both of whom supported rapid withdrawal from Vietnam.
However, like I said, at the time, most delegates were picked by state party leaders, and Humphrey, even though he didn’t participate in any of the primaries, had won over the support of the state partie. Meanwhile, although most Kennedy supporters backed McCarthy, not all did. So, after everything, Humphrey went into the convention with enough delegates to get the nomination.
A lot of the antiwar Democrats, especially the college students who made up a really vocal segment of Kennedy/McCarthy supporters, were upset by this, and there were protests in Chicago by thousands of antiwar protesters outside the convention. They were upset both because they associated Humphrey with the Johnson administration who they blamed for the war, and also because he had been nominated without entering any primaries, so they felt that the “voice of the people” wasn’t being heard.
The mayor sent police to try to break up the protest and it led to violence, as the protestors resisted the police and the police attacked the recalcitant protestors. 8 people were arrested afterwards and charged with incitement to riot (“The Chicago Seven”), and that’s an interesting story if you’re interested in looking it up.