Emily Dickinson was known for being a hermit and did not often go out into the world. As such, she was used to being an individual who went against the crowd. When she speaks about the Majority, she is basically referring to the majority of people. For example, when people refer to "popular opinion," they are referring to what the majority of people think or say.
In "Much Madness is divinest Sense," Dickinson argues that the definition of sane or insane is decided because everyone (the Majority) agrees it is so. She says that just because everyone (the Majority) thinks something or someone is crazy, doesn't necessarily make it true. However, too often something becomes true just because the Majority believes it. She says that truth is not necessarily decided by popular opinion (the Majority).
In "The Soul selects her own Society," Dickinson says that she likes only the people she connects with. That is, her soul likes certain people and she has barred the door to everyone else. Even if "the Majority" likes someone, she doesn't care. She doesn't want to interact with the majority of people, and she doesn't want to be friends with someone the majority of people like. She says that she is unmoved by an Emperor and will let him stay outside.
When Dickinson references the Majority, she is referring to everyone, or society in general.
