Tap your account avatar at the top-left of the screen to open the Folder Drawer.
Your folders for the current account are listed there — provider (system) folders like Inbox, Drafts, Sent, Trash, Spam, Outbox, and Archive/All Mail appear first, followed by your custom folders. Custom folders can be renamed, deleted, or created.
On a tablet or desktop you can also hide or expand the folders pane to give the mail list more room.
If you have multiple accounts, see your Unified Folders to view folders across all of them at once.
Note: There is no per-folder sync switch in BlueMail. What you can change is how far back mail is kept on the device, which for an Exchange-family account is a single setting — see Folder sync for Exchange accounts and Offline Storage.