Use the Resolve button once you’ve finished addressing the contact's question or concern. Resolving tells your organization that no further response is required. Your Conversation List shows Open Conversations by default, so a Conversation you Resolve drops out of the list. To find it again, set Status to All.
The Conversation will automatically re-open if the contact responds again. You can always re-open a Conversation on your end as well.
Watch the tutorial on Messaging Basics here.