to move out from within something: to go out, come out, or stream forth from a source
This verb pictures motion outward from inside a place, a person, or a thing. It is the base verb for going or traveling ("to go, proceed") with a prefix meaning "out of," so it always keeps the sense of coming out from somewhere. The many ways it is used all trace back to that single picture.
Most often it describes people on the move: crowds streaming out to be baptized, Jesus and his followers leaving a town or the temple, someone setting out on a journey. From there it stretches naturally to anything that issues from a source. Words come out of the mouth. Evil comes out of the human heart. In the visions of Revelation, fire, a sword, lightning, and a river of life all pour out from a mouth or a throne. And in one weighty saying of Jesus, the Spirit of truth comes out from the Father.
Because the form used throughout the New Testament often carries a continuous, streaming quality, the word tends to suggest not a single step out the door but an ongoing flow. That is why it fits both a river issuing from a throne and a steady procession of people coming and going.
English has no single verb that covers all of this, so translators rotate among "go out," "come out," "proceed," "come forth," and "depart," choosing whichever fits the source and the thing that leaves it.