Mathoms are any items that Hobbits had in their possession but had no immediate use for and didn't wish to throw away.

As a people, Hobbits love giving gifts, especially on their birthdays, and as a result they all tended to accumulate so many mathoms that their dwellings became cluttered. Many mathoms were passed around so often that it was not known from where they originated.

Mathoms so influnced the Hobbits that they named the Museum in Michel Delving the "Mathom House".
Encyclopedia entry originally written by PotbellyHairyfoot