Mathom was the hobbit term for anything which they had no use for but were unwilling to throw away. Their holes and houses usually were quite crowded with mathoms. Hobbits were very fond of giving mathoms to one another; on birthdays, it was tradition that the hobbit who had the birthday would give a gift to anyone who attended his party. This way mathoms travelled from hand to hand often around the whole Shire and sometimes finding their way back to the original owner. Weapons and other gear of war was usually looked upon as mathoms in the Shire and usually they became trophies hanging over fireplaces or on walls.
Museums in the Shire were called Mathom-Houses. The most significant one was at Michel Delving. Bilbo Baggins loaned his Mithril mail to be displayed there, which shows the extraordinary character of hobbits. Even if a suit of armour was made of the most precious metal in all of Middle-earth and set with white gems, it still did not have any practical use and was thus regarded as a mere mathom.