Coming out is the generally understood to be the act of an individual confirming something about themselves that was previously unknown, unconfirmed, or unspoken. While the term is usually associated with being transgender, gay or lesbian, it can also apply to being HIV-positive.
One comes out to confirm an identity that is considered unacceptable which is why one hides it. When someone comes out for the first time, the narrator may be revealing something fundamental about herself that she had hidden to avoid repercussions like getting fired, thrown out of her home, being humiliated or rejected.
When we come out to a brother, co-worker or friend, the anticipated response carries added weight. The impact of that response is charged by the depth of the relationship. The value we assign it is scaled by what that person means to us and what we seek from them.