perichōros

Greek already had a plain word for a country or a stretch of land, χώρα. This one adds the idea of "around". It never names a district on its own terms; it names the land that lies about some center, so the sentence has to say what the center is. In the Gospels that center is a river, a lakeside town, a province, or a pair of cities, and the word takes in whatever farms, villages, and open ground surround it.

That is why it turns up so often in sentences about something spreading. It measures reach, the distance a crowd walks in or a report travels out:

• word about Jesus runs through the whole countryside around Galilee (Mark 1:28)
• a report about him reaches every place in the surrounding country (Luke 4:37)
• what people are saying about him carries through Judea and all the country around it (Luke 7:17)

Because the land and the people on it are hard to keep apart, the word can slide from one to the other. When Matthew writes that Jerusalem, Judea, and all the country around the Jordan went out to John, he means the crowds who lived there, the way we say a whole town turned out. Hebrew called the round plain along that river the כִּכָּר, and the old Greek translation of Genesis used this very word for it, which is part of why the phrase sounds so settled in the Gospels.

A different word, ὅριον, names territory by its boundary lines, the land that belongs to a particular city or people. This word draws no lines at all. It simply points outward from a place and gathers in what is near.