1.
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.
See regift, white elephant, junk, fruitcake
2.
A term coined by JRR Tolkien, meaning an object given as a present to someone who does not want it. This person then gives it to someone else at an appropriate occasion. The object passes to the majority of people in the area over time, becoming a mathom.
In these days of commercialization, no one thinks to use mathoms as Christmas presents...
