Closing/deleting or leaving a Channel is done from the dropdown which appears in the middle of your screen when you click into a discussion.
Internal Channel - anyone on a team channel can close it (or reopen it). This moves it to your closed list which is accessed from the menu on the top right of your screen. You cannot have a conversation on a closed team channel but you can reopen it at any time.
Private Channel - Only leads can close a private channel. This moves the channel to the closed list for all the participants in your group. It is still possible to converse in a closed channel, and all contents continue to be searchable.
You can leave a channel at any time and it will disappear from your interface. You can always re-discover it later if it is an internal channel. If you leave a private channel (or are removed), you will lose access to its contents and the channel will be removed from your interface. You cannot leave if you are the only lead.
Deleting is permanent and cannot be easily recovered. If there is content that you may wish to access in the future, it is better to close it.
Internal Channel - These can only be deleted by admins.
Private Channel - Only leads can delete a channel which removes all access to the content for all members of their group.