Too many open tickets may cause rendering issues eventually - so it is advisable that once you no longer need a specific conversation to be open you may archive it.
To archive a ticket, click the Archive ticket button to the top-right corner of the center panel. This will prompt a new window:
Fill in the agent ID (typically your own), select one of the available reasons and press the now lit Archive button. Archiving a ticket will remove it from your left panel list, so you won't be able to view, reopen or take any new actions on it.
The ticket will still be available for monitoring when looking for it in the Audit tab.