the.com/toothbrush holder

means A small stand or cup, usually mounted by a sink, designed to keep toothbrushes upright and off the counter between uses.

from No mystery here — it's a straightforward compound of 'toothbrush' (itself 'tooth' + 'brush,' a word for a bristled cleaning tool traced back through Old English and Germanic roots) plus 'holder,' from 'hold,' an old Germanic verb meaning to grasp or keep. The toothbrush as a mass-produced object is largely a 19th- and 20th-century story, and its little bedside companion, the holder, followed as plumbing and bathroom design domesticated oral hygiene — a plain functional name for a plain functional object.