You can easily mark, move, or delete an email in your iPhone's Mail app from within the body of an email using the menu at the bottom of your screen. You can also easily manage individual emails from within your inbox by swiping to the left over the email. But this is tedious and unnecessary if you have a large number of emails to deal with.
To mark, move, or delete multiple emails at a time, go to your inbox and tap edit in the upper right corner.
Tap on each email to select it (or tap Mark All in the bottom left corner to select all your emails.)
Once you have all the emails you want selected, tap Mark, Move, or Trash.
Tapping Mark will let you flag the email, mark it as read, or move it to junk.
Tapping Move will bring up a list of folders to which you can move the email.
Tapping Trash will delete the selected emails.
If you mistakenly mark an email as junk, move an email to the wrong folder, or delete the wrong email, just shake to undo.