connecting subfolders in mac mail - can't see how

I recently connected my computer's mac mail to my online webmail but all my online subfolders have not come down onto my computer. I have a lot of emails already filed in them online for my business but have limited space and thus I finally set up mail on the computer. I don't see where to get those to download and be on my laptop. Is this possible?

Thanks!

via ehMac.ca https://ift.tt/2MpbRc6