Izumo Shrine is located in Shimane in Japan. It is a Shinto Shrine well known for those who want ot pray for a good marriage.
Shintoism is the native religion of Japan. Those who practice Shinto believe in kamis or spirits that live in nature. When worshipping at a Shinto shirne, one must make and offering,clap 3 times, and bow. The clapping alerts the spirits to your presence. People also leave emas or little plaques with prayers and requests for divine intervention.
I imagine this couple was praying together for a good marriage!