The concept is very similar between those two, which means that someone enters specific space. But the usage is differenct, and it depends the view, who says the scene. I give you some example to understand the difference between 들어가다 and 들어오다. If I enter my brother's room, I can say 나는 동생 방에 "들어간다". If I see my brother entering my room, I cant say 동생이 내 방에 "들어온다". I am not sure whether you can get what I want to say. I hope you do.

It depends on the direction of movement from the speaker 가다 means "to go away from the place where is the speaker" 오다 means "to come close to the place where is the speaker" 들어오다 means "to enter a place where is the speaker" 들어가다 means "to enter a place where is not the speaker"