A party convention in which delegates are able to vote for the candidate of their choice, and are not tied to the results of primaries or caucuses.
Open conventions were the norm until about 1968. The Democratic Party’s delegates were never tied to primary votes before then, and could choose who they wanted (the Republican Party was tied to primaries much earlier). This led to many cases where candidates would forego primaries and focus on delegates instead.
According to Reuters, “the 1968 election, when Hubert Humphrey, who eschewed the primaries in favor of courting officials who controlled the delegates, lost to Republican nominee Richard Nixon, led to reforms that essentially gave control of the nominating process to the popular vote. A number of states decided the easiest way to comply with the new rules would be to hold primaries.”
Today, open conventions only happen when no candidate takes a majority of the delegates. The last open convention was in 1976, when neither Ronald Reagan or Gerald Ford was able to secure a majority of GOP delegates. The delegates were then free to choose a candidate without being tied to a vote.