What do non-trinitarians mean when they call Jesus the "Son of God"?

I can answer this for one particular group of non-trinitarians: the "Swedenborgian" denominations that accept the Christian theology of Emanuel Swedenborg (1688-1772). Swedenborg rejected the traditional doctrine of the Trinity, saying that God is not three persons, but one person, in which the Father, Son, and Holy Spirit are three "essential components" (Latin essentialia). (For a Swedenborgian presentation of the Biblical basis against the doctrine of the Trinity, along with a brief explanation of Swedenborg's non-trinitarian doctrine of the Father, Son, and Holy Spirit as together constituting one person of God, see: What is the Biblical basis for disbelief in the doctrine of the Trinity?)

For those who accept Swedenborg's theology, "the Son of God" is not a separate person, but rather the human manifestation of God's eternal divine nature (which is called "the Father" in the New Testament). "The Son of God" is also the divine truth, which is called "the Word" in John 1:1, 14:

In the beginning was the Word, and the Word was with God, and the Word was God. . . . The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.

Here is how Swedenborg states the meaning of "the Son of God" as God's human manifestation, in True Christianity #92:

The "Son of God" is the human manifestation in which God sent himself into the world. The Lord [Jesus] frequently says that the Father "sent" him, or that he "was sent" by the Father (for example, Matthew 10:40; 15:24; John 3:17, 34; 5:23, 24, 36, 37, 38; 6:29, 39, 40, 44, 57; 7:16, 18, 28, 29; 8:16, 18, 29, 42; 9:4; and very often elsewhere). The Lord says this because "being sent into the world" means coming down among people, which he did through the human manifestation he took on through the Virgin Mary.

The human manifestation really is the Son of God, in that he was conceived by Jehovah God as the Father, as it says in Luke 1:32, 35. (links added)

Here is how Swedenborg states the meaning of "the Son of God" as divine truth, in Arcana Coelestia (Secrets of Heaven) #7499 (in a somewhat archaic translation):

In the Word [the Bible] the Lord is called "Jehovah" in respect of Divine Goodness, for Divine Goodness is the Divine itself, and the Lord is referred to as "the Son of God" in respect of Divine Truth. For Divine Truth goes forth from Divine Goodness, as the Son does from the Father, and is also said to be born from it. But something more must be said to show what this implies. When the Lord was in the world He made the Human He had assumed Divine Truth, and at that time called Divine Goodness, which is Jehovah, His Father. He did so because, as has been stated, Divine Truth goes forth and is born from Divine Goodness.

In other words, "the Father" is the divine good, or the divine love; and "the Son" is the divine truth, or the divine wisdom. Together with the Holy Spirit—which, in Swedenborg's theology, is "the divine proceeding," or in contemporary language, God's love and truth flowing out into the universe with power—these three "essential components" constitute the single person of God.

I agree with previous answers, but I would like to take a look at a different angle of the question.

Asking about "non-Trinitarians" is extremely broad, since there are many groups from many different time periods. I will focus on one (albeit still extremely broad) group, namely, what would a (hypothetical) person in the Ancient Near East from the Israelite/Jewish people think when they heard or read of an individual (such as Jesus) being referred to as a "son of God" or even as a "god/God". There were a number of different types:

1. Powerful angelic beings, usually those who made up God's inner council/ministry/cabinet (Job 1, possibly Psalm 82:1, 6 and Deuteronomy 32:8 LXX). In the Enochian school of thought, Enoch son of Jared ascended to heaven and was transformed into the angel Metatron (Similtudes of Enoch), who was referred to as the Lesser (or Little) LORD (3 Enoch). One of his other angelic names was Yahoel, a combination of the divine names for God and LORD, and he was believed to be the angel whom God's Name resided within (Exodus 23:20-21). The "sons of God" in Genesis 6:2-4 may refer to angels or human beings, the passage has been interpreted both ways historically: e.g., the Enochian school considered them angels (see 1 Enoch), while rabbinic opinion generally considered them humans. The "us" in Genesis 1 on the other hand is rabbinically interpreted as God speaking to the divine council (see Bereshit Rabba on Genesis 1 and 6).

2. The entire people of Israel as a single corporate entity (Exodus 4:22; Hosea 11:1; 4Q504 1-2) (hence every single Israelite being a son/daughter of God, cf. John 8:41-42), over time this was expanded to cover all members of the entire human race (Pirke Avot 3:15, 5:20; Mishnah Berachot 5:1; Midrash Megilla Rabba 10). This appears to be the model for members of the early Christian community referring to themselves as "sons of God": e.g., "But to all who did receive him, he gave them the right to be sons of God" (John 1:12).

3. A king of Israel, particularly a king of the Davidic line was referred to as a god/God (elohim) (Psalm 2:7-8, 45:6, cf. 89:27-28; 2 Samuel 7:14; 1 Chronicles 17:13; 4 Esdras 7:28-29, 13:32, 37, 52, 14:9). Moses, the original ruler of the Israelite nation, is also compared to a god/God (elohim) by God (Exodus 7:1). Samuel, a later ruler of Israel, is referred to as a god (elohim) coming up from the earth, by the witch of Endor (1 Samuel 28:13).

4. A powerful person such as a judge or ruler, or group thereof (Exodus 21:6, 22:7-9; Psalm 82:1, 6). Many non-Jewish rulers in the Ancient Near East also frequently referred to themselves as sons of their deities (for more information, see Martin Hengel's "Son of God: the origins of Christology").

5. An extremely righteous person (a 'pious one', 'righteous one', 'just one' etc), who by their exceedingly high level of virtue and good works prove themselves to be of similar nature to God and are even in effect "adopted" by God; see Wisdom of Solomon 2:13, 16, 18, 5:5; Sirach 4:10.

6. Miracle-workers, who mostly wandered from place to place doing miraculous wonders, in the manner of Elijah and Elisha (hence often referred to as "men of deeds", see e.g., Mishnah Sotah 9:15) - Hanina son of Dosa (Bavli Taanit 24b, Berachot 17b, 61b), Hanan the Hidden (Bavli Taanit 23b), Honi the Circle-drawer (a.k.a. Honi the Righteous) (Mishnah Taanit 3:8; Josephus Antiquities 14.2.1), Abba Hilkiah (Bavli Taanit 23a, b), and Rabbi Meir, who was known as baal ha-ness (meaning, "lord of the miracle") (Mishnah Sanhedrin 6:5). For more information, Geza Vermes has written a series of books on this topic (the most well-known being "Jesus the Jew"). The most famous of these miracle-workers was Rabbi Simon son of Yochai (he was later referred to not only as God's son, but explictly as the LORD, and that his mouth was the LORD's mouth, etc; see Zohar 1:223a; 3:59b, 201b).

7. A person directly created by God, and hence has no other progenitor - i.e., Adam (Luke 3:38).

(On a side note, there are two women who were referred to explicitly as "daughters" of God, both of whom were Egyptian. (1) Batya/Bithiah the daughter of Pharaoh, who adopted Moses [see Exodus 1]. Her name even means "daughter of the LORD". [See Leviticus Rabba 1:3] (2) Asenath, the husband of Joseph [see Joseph and Asenath]. Although later tradition considered her the granddaughter of Jacob [Pirkei d'Rabbi Eliezer 35, 37]. In addition, the Law of Moses itself was personalized and considered to be the Daughter of God [Vayikra Rabba 20] and Wisdom referred to in Proverbs 3.)

In short, a Near Eastern non-Trinitarian could consider Jesus as any of these types of "god/God/son of God", except (7). (e.g., the book of Hebrews appears to be directed, at least in part, to a group of people who considered Jesus to be an angelic being, see chapter 1.)