The meaning of the Hebrew word "goyim" is somewhat obscured by its alternate translations as "heathen," "nations," and "Gentiles." This is also true of the equivalent Greek term "ethne" and its variations.
Today, "heathen" means something like "unchurched, primitive pagans." "Nations" now carries the governmental sense of the nation-state, a modern phenomenon. "Gentiles" means those who are not Jewish. In combination, these different connotations come close to portraying what "goyim" actually means. But there are goyim in the world today who do not have their own state or government. There are also goyim who are neither unchurched, primitive, nor pagan.
English translations of the Bible and of early Church writings tend to use "heathen(s)" or "nations" for "goyim." This is unfortunate, because it makes it very difficult for readers to understand the nature and intensity of the conflict in the early Church over the manner in which goyim (i.e., Gentiles) could be saved. (cf. Acts 15) It makes it difficult to appreciate what a radically new thing God was doing. It makes it difficult to appreciate both the nature of the Great Commission and the full measure of God's grace.
Some who deal with the Church in different cultures use "people-groups" to more accurately convey the Biblical meaning of "goyim" and "ethne." This is much better, but it still does not convey the radical difference between Israel and the goyim. Though God promises to make Israel a holy nation ("goy kadosh"), He makes it clear that Israel is a unique people, not to be "reckoned among the goyim." (cf. Ex. 19:6, Num. 23:9) For our purposes, "Gentiles" or "goyim" will be primarily used to denote the Hebrew "goyim" or Greek "ethne" and their variations.