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Wiktionary
shoe tree

alt. A device approximating the shape of a foot that is placed inside a shoe when it is being stored to preserve its shape and extend the life of the shoe. n. A device approximating the shape of a foot that is placed inside a shoe when it is being stored to preserve its shape and extend the life of the shoe.

Wikipedia
Shoe tree

A shoe tree is a device approximating the shape of a foot that is placed inside a shoe to preserve its shape, stop it from developing creases and thereby extend the life of the shoe. It is a reusable alternative to wadded rags or newspapers.

Perhaps more important than maintaining the shape, shoe trees also play a crucial part of wicking away leather-damaging moisture from the inside. Shoe trees are especially important if you do not wear socks with your shoes as all the sweat will be absorbed by the leather and can lead to lining rot.

Higher quality shoe trees are made from solid wood, usually cedar, which helps control odor and absorb moisture. Other materials include beech, lime and alderwood. Although most shoe tree manufacturers claim that cedarwood is superior, there is really no difference as long as the shoe tree is made of unfinished wood.