The "leaf" in the expression, "to turn over a new leaf," is actually from a book - not a tree, as often believed. It refers to a blank page in a lesson book or book of precepts where one can begin work anew, all toward improving or amending one's conduct.
A page in a book was at one time called a leaf because the leaves of certain plants, such as the palm tree, were used as ancient manuscript paper. To begin a new life or a new way of thinking meant to turn a palm - or one of these pages where deeds and misdeeds were dutifully recorded.
Turning over a new leaf means putting the past behind and moving on to a clean page. By extension, the modern expression "being on the same page" means feeling comfort in a common life experience or way of thinking with someone.
SOURCES: 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; 'Heavens To Betsy!' by Charles E. Funk; 'Have A Nice Day,' by Christine Ammer; 'Loose Cannons and Red Herrings,' by Robert Claiborne.