@imdtckdkr,
http://www.word-detective.com/2008/08/14/leaves-table/
Quote...
"One of the uses to which “leaf” was put in the 15th century was to mean “a hinged part or a part attached at one edge by a hinge,” as a hinged flap on machinery, furniture or the like. For example, the parts of a “Dutch door” (also called a “stable door,” divided horizontally to allow opening the top half while the bottom remains closed) would be considered “leaves.”
By the 16th century, this sense of “leaf” was being applied to hinged sections of a table that hang down from the side but can be raised when more surface area is needed. Within a hundred years, this sense was expanded to include any movable element or addition to a table, such as the “leaves” that are inserted into the top of a table to increase its area."