It is a way of saying "I have something additional to talk about." It may have something to do with what has been said before in the conversation, but perhaps not. It can be a way of changing the subject. "By the way, what ever happened to Jane after she graduated?" "By the way, we're having a party on Saturday and would like you to come."

by the way = something else to say

Anyusbor, "By the way" significa "por cierto", "a propósito". Ejemplos: By the way, did you call Karen last night? = A propósito ¿llamaste a Karen anoche? She is, by the way, the person who gave us the report last week Por cierto, ella es quien no dio el reporte la semana pasada. Espero que eso te ayude, saludos.