This is possible for IMAP and EWS accounts, as POP3 does not allow server side folder access.
Here is what the FAQ says about it (and I really could not have said it better myself):
http://www.aqua-mail.com/?page_id=227As of 1.2.3.0, you can access folders on an as needed basis:
This can be done from the title bar of any folder’s message list (last item in the dropdown is “Other folders…”), when moving messages, in the account list in two panel mode.
When accessing folders this way, recently accessed ones (up to three) will be shown in the folder list drop-down and the account list (if the per-account setting mentioned above is enabled). They are removed from the recent list automatically, after one week (can be changed in app settings) or, as of 1.2.5.0, you can long press a “recent” folder to clear it.
Please note that the “Other folders…” entry is shown by default on tablet sized devices only. On phone sized devices, please long press an account, choose “Options and Folders”, then “Account options”, scroll to the end and enable “Show Other folders…”.
The second way to access a folder is to set it to sync (every time the app checks mail in the account), which will make it always show in the account list (“main window”) for easiest access.
To do this, long press the account in the main window, choose “Options and folders”, then “Folders”. Tap a folder, choose how it should be synced (most likely just “As incoming” since “special” folders like Sent, etc. are usually set up automatically). Each incoming folder is presented in the UI separately.
Finally, if you delete any folders that are set to sync in the app (using web mail, or another mail app), please bring up Account Options / Folders in Aqua Mail to sync its folder list with the server.
