Archiving a conversation is useful to filter out conversations that you don't want to see in your inbox. You can then filter out this conversations though your inbox filters.
There are 2 main ways to Archive a conversation: The first method is to archive a conversation from the conversation header menu and clicking on Archive. Alternatively you can archive a conversation from the conversation sidebar by clicking on the icon.
You can also archive conversations automatically by turning on the Archive conversations when closing them? option on your inbox settings.