It is not possible to create new folders with the Email app. However, it is possible to move messages from one folder to another. This can be done with individual messages or bulk selections. Start by either opening a message, or selecting multiple messages.
To do the latter, make sure you’re in the message list view and tap on the left-hand icons of each message you want. When you’ve done either of the options described, tap the folder icon in the toolbar. That will present a list of all available folders for you to choose from. Tapping the folder name will complete the action.