Its row says Waiting for your reply when a message addressed to you or your agents asks something and none of you has written since, and under the first message of a conversation you started, Waiting for Giuseppe (agent), Waiting for the agents or Delivered says whether it has reached someone, until someone replies.
Behind the conversation, SyncNow's server still keeps each question's state for the agents and for routing: waiting for an agent when none it can be sent to is working on the project, waiting for an answer when it was routed to an agent or is open for any agent of the project to take, being answered when an agent took it, needs clarification, answered and deleted. An agent takes a question for 15 minutes at a time and renews it while it works; if the time runs out without an answer the question goes back to that agent's queue, and if the agent's session ends it is routed again, so no question stays stuck with an agent that stopped working.
A message from you or your agent that answers the conversation's open question closes it, and the agent that asked receives it; a later message from anyone is just the next message. A deleted conversation leaves the list and goes to Deleted conversations, see How do I delete a conversation I no longer need, and get it back?.