A brown shower is one form of coprophilia. Coprophilia is a very extreme, somehow abnormal interest in human excrement. It is often combined with sexual acts.
If someone uses another one as a human toilet you can call this act a brown shower. Domination and humiliation are main aspects of the sexual preference so you can often find it in the BDSM scene. Mostly women will take the dominant part and a (helpless) male slave is her submissive victim. Most of the time the golden shower itself is used to punish the slave but sometimes it is also a way to reward the slave if he is strongly addicted to the excrement of his mistress.
The mistress sits above the slave and she poops at his head. The slave often has to eat her shit so she scats directly into his mouth. Sometimes the slave has to chew the shit and sometimes it only lands at his head. You can find lot of different variations.