Most email service providers allow email messages to be organised in to groups. If the email service you use allows this, then the Mail app on your iPhone or iPad will allow you to create groups and to organise messages by placing them in groups. The name by which groups of messages are known varies; sometimes they are called folders, but the Mail app refers to them as mailboxes so that is the term used here. These instructions assume that you are using VoiceOver.
Note that the precise instructions given here may be slightly different from what you experience. If necessary, please swipe or feel around the screen to locate the desired button.
To create a new mailbox, you need first to decide where you want to create it. If you have multiple email service providers, then you need to decide which provider will hold the mailbox. Also, mailboxes can be created inside other mailboxes. To begin to set up the new mailbox you need to get to the screen showing the list of all your current mailboxes. Feel near top left of the Inbox screen for the back button. You will hear "Mailboxes, back button". Now double tap to go to the list of mailboxes. Feel near top right of screen on an iPhone or top middle on iPad for the Edit button and double tap. Next feel near bottom right on iPhone or bottom middle on iPad for the "New Mailbox, button" and double tap. Enter the mailbox name using the keyboard, dictation or handwriting. Now slide your finger up the centre of the screen from the keyboard until you hear "Mailbox location, heading". Lift your finger and swipe right. You may just hear button. Double tap. Swipe right to find the location in which you want to place the new mailbox, for example you might choose iCloud or Gmail. Now double tap. Now feel near top right or middle of the screen for the "Save button" and double tap. That will take you back to the Edit screen. Feel near top right or middle for a "Done, button" and double tap. You should now be at the Mailboxes screen. Swipe right to Inbox or All inboxes and double tap to return to your list of email.
On the Inbox or All Inboxes screen, feel near top right on iPhone or top middle on iPad for the "edit, button" and double tap.
Now swipe right to find the message you want to move and double tap to select it. If you want to move multiple messages to the same mailbox then continue to select additional messages.
Next find the "Move, button" in the toolbar at the bottom of the screen and double tap. Swipe right to locate the target mailbox and then double tap. This will move the message or messages and return you to your list of messages.
An alternative to using the Edit button from the Inbox list is first to open the message you want to move and then use the "move, button" in the toolbar at the bottom of that screen. Only the current open message can be moved using this method.
Drag and drop can also be used to move single messages from the Inbox list. Locate the message you want to move and swipe up until you hear "drag item" and double tap to initiate the drag. You will hear a triple rising tone. Next use the "mailboxes, back button" at top left to view your list of mailboxes and locate the mailbox to which you want to move the message. Swipe up until you hear "drop onto item" and then double tap.
Finally, you may wish to delete a mailbox that you no longer have a use for. Deleting a mailbox deletes both the mailbox and the email messages within it. To delete a mailbox, go to the Mailbox list as in the first step for creating a new mailbox. Find Edit and double tap. Swipe right until you reach the mailbox that you wish to delete and then double tap. Swipe right until you hear "delete mailbox, button" and then double tap. A pop up will appear explaining that deleting a mailbox removes its messages from your account. Messages deleted in this way are deleted irreversibly. Swipe right to the "delete, button" and then double tap. Find the "done, button" at top right or centre and double tap to complete the changes.