A bounded space within a larger dwelling, given over to one purpose. Also the space available for a thing to exist in.
Old English rum (space, extent, an open area), from Proto-Germanic *rumaz, from a Proto-Indo-European root meaning to open, make room; the bounded chamber and the abstract space to move in are the same old word.
A bounded space given over to one purpose, and also the plainer thing every purpose needs first — enough space in which to exist at all.