heaven: the realm above the earth, whether the visible sky overhead or the unseen place where God reigns.
One Greek word covers a span that English splits between two or three words. At one end it names the physical sky, where birds fly, weather forms, and sun, moon, and stars appear. At the other end it names the place where God lives and rules, above and beyond anything we can see, where Christ ascended and from which he will return. The New Testament writers move freely along this range, sometimes within a single passage, because in their world the sky overhead and God's dwelling were not two unrelated places but the lower and upper reaches of one reality above the earth.
A few times the word does more than name a place: it stands in for God himself. When people ask whether John's baptism was "from heaven or from men," or when the prodigal says he has "sinned against heaven," heaven plainly means God. This was a recognized way of speaking among Jews of the time, and the New Testament uses it, though only in a handful of clear cases rather than as a settled habit of avoiding God's name.
The plural form, "the heavens," appears often, especially in Matthew. This is an ordinary feature of biblical Greek picked up from the Greek Old Testament, which sometimes rendered the Hebrew word for heaven (itself plural in form) with a Greek plural. The plural does not by itself signal a grander or different place; the word means the same thing whether singular or plural. Several New Testament books do, however, picture heaven as layered, or as something Christ passed through to reach God's presence, and Paul once reports being caught up to "the third heaven" without explaining what the rest of the map looked like.