gallery (theatre); upper balcony
Specifically the upper, cheaper seating area in a traditional theatre, especially kabuki. The term is strongly associated with kabuki culture.
歌舞伎座の大向こうから掛け声が飛んだ。
A shout came from the gallery of the Kabuki-za theatre.
audience (theatre); the masses; general public
By extension, the audience in the gallery, often seen as representing the common people or popular opinion. Can carry a nuance of the 'man on the street' or the general public's view.
彼の演技は大向こうをうならせた。
His performance impressed the audience.
その政策は大向こうには受けが悪い。
That policy is unpopular with the general public.
Standard spelling.
Irregular okurigana variant; less common but seen.
Compound of 大 (おお, 'big') and 向こう (むこう, 'opposite side'). Originally referred to the large seating area opposite the stage in traditional theatres, hence the gallery.