When I grew up (which was, for reference, was in the 1990s and the Pacific Northwest), "going out" was the generic, vague yet very important term for the basic level of male/female adolescent relationships.
There was no specific level of commitment or activity that were required to "go out". The main thing about "going out" was the nerve, tension and resolution of asking and confirming the status. While adolescent infatuation and experimentation are hardly new, I think that some of the conditions of "going out" were specific to my era. Perhaps most importantly, dating, as a ritual, is something that people of my generation, whether they are 13 or 30, don't seem particularly interested in. Thus, "going out" despite the derivation of the term (and see below), does not mean a commitment to date each other, so it is not quite the same as the 50ish, "going steady".
The term probably comes from "going out on a date", although (especially in the early years of adolescent), no one actually dated, since most meals, movies, or general frivolous activities were done in nervous pack groups. Theoretically, if such an occasion were to arise, the level of commitment of the boy and girl (and when I was growing up, it was a boy and girl thing) would mean that they would be the ones to accompany each other. And yet, the term going out meant more than that.
My own feeling was that the term comes more from the fact that the emotional atmosphere of adolescence seems like a storm tossed sea, where every moment is a shadowy tumult of confused intentions and misdirection and anxious questions about other's motives. When two people "go out", they are rising above and out of that vast sea, their emotional commitment providing a shining pillar of certitude and emotional trust from the ambiguity and isolation of solitude. At least for a week, or at the outside a month or so.