how many emails does my mac book air archive hold? I am saving emails in the archive option on my  macbook air. 

What is the quantity limit??
I doubt you'll reach a limit.

HFS+ which stores the file limits you to 2.1 billion files in a folder so you could have a lot of emails stored to archive. When you go to archive them, that one file holding billions of messages could grow to a size of 8 EB (and one exabyte is one million terabytes) so there's really little chance Mail app will prevent you from archiving an absurdly silly number of messages.