Weather Hutch
Japanese Living

this is a "hyakuyoubaku" more commonly translated as a "Stevenson Screen". A weather hutchcontains weather gauges (barometers, thermometers, thermographs, etc) and was designed by the father of famed British writer Robert Louis Stevenson.

Relevance to Kyokai no Rinne

In the series, Rinne uses the school's weather hutch as a communication device between himself and the student body. A student will leave offerings to Rinne in hopes that he'll take on the job of exorcising whatever local ghost that may be troubling the student.