A regift. A relatively trivial object that has repeatedly been given as a present. Strictly, a mathom is
probably NOT an object with a tendency to decay (i.e. fruitcake), nor an object of obviously poor
construction (i.e. a crooked handmade sweater or junk), nor a family heirloom or a useful "hand-me-down" article (i.e. toddler clothing), nor one which requires expensive upkeep (i.e. a large, exotic pet -- a proveribial white elephant).
Such objects most likely persist because they are slightly too valuable or unusual to dispose of outright or give to Goodwill, yet have such limited use or appeal that few wish to retain them. Modern-day candidates for mathomhood are commonly visible in catalogs for novelty
electronics, pop art, junk jewelry, and sports memorabilia, as well as in roadside "local" gift stores.
"It was a tendency of hobbit-holes to get cluttered up; for which the custom of giving so many birthday-presents was largely
responsible. Not,
of course, that the birthday-presents were always new; there were one or two old mathoms of forgotten uses that had circulated all around the district; but Bilbo had usually given new presents and kept those that he received."
-- J.R.R. Tolkien, The
Fellowship of the Ring, p. 65.