Within Teamwork Chat, conversations are intended to be short-lived. An example of a conversation might be a discussion about where to go to for lunch today.
Once you turn a conversation into a channel (by giving it a title), you're giving it more importance. A channel is designed to be used over an extended period of time (i.e. something you will come back to again and again). An example channel might be a "Marketing" channel.
Both conversations and channel appear in the Timeline view of the sidebar, in reverse chronological order. That is, the conversations or channels with the most recent messages will be at the top of the list. Inactive conversations will drop lower and lower over time, falling below other (more active) conversations or channel.
For more information see: Creating a conversation/channel