A fainting room was a private room, of which its main features/furniture were fainting couches, used during the Victorian era, to make women more comfortable during the home treatment of female hysteria. Fainting rooms were used for more privacy during home treatment pelvic massages. Such couches or sofas typically had an arm on one side only to permit easy access to a reclining position, similar to its cousin the Chaise longue, although the sofa style most typically featured a back at one end (usually the side with the arm) so that the resulting position was not purely supine.
Theories for the prevalence of fainting couches
One theory for the predominance of fainting couches is that women were actually fainting because of their corsets were laced too tightly, thus restricting blood flow. However, pictures from the 1860s show women horseback riding, playing tennis, and engaging in other vigorous activities in corsets without hindrance. This being stated, though, a tightly-laced corset does restrict airflow to the lungs. As a result, if exerted herself to the point of needing large quantities of oxygen, being unable to full inflate the lungs could contribute to a light-headed state; exacerbating this state could surely lead to fainting. Alternatively, a high state of emotions could result in hyperventilation, potentially resulting in the same event.
The second most common theory for the predominance of fainting couches is home treatment of female hysteria through manual pelvic massage by home visiting doctors and midwives. As a "disease" that needed constant, recurring (usually weekly) in-home treatment with a procedure that through manual massage could sometimes take hours, creating specialized furniture for maximum comfort during the extended procedure seems likely, as does the later creation of fainting rooms for privacy during the intimate massage procedure.