Mathom was the hobbit term for anything they had no use for but were unwilling to discard. Their holes and houses were crowded with these. 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 their party attendees. This way, mathoms travelled from hand to hand often around the whole Shire, sometimes finding their way back to the original owner. Weapons and other gear of war were usually considered mathoms in the Shire, often becoming 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 coat of mithril mail to be displayed there.