I take it to mean upsetting the flow of conversation.

For example, suppose you're at a party, talking in depth about a football team's season and they say something unrelated like "Oh by the way have you seen John?". It is usually a polite way to try to wrap up a conversation. A polite response would be something that graciously gives them permission to change the subject or leave, for example, "I think I saw him outside, maybe go take a look?".

Sometimes it takes the form of bored body language and sentences that don't lead the conversation onwards, e.g. "Yeah that's crazy" or "Well, what can you do...". In that scenario I like to give the conversation a respectable death, e.g. "Well, all we can do is hope for a better season in 2027!".