In Zec. 3:2, what is the meaning of "a brand plucked from the fire" (אוּד מֻצָּל מֵאֵשׁ)?
וַיֹּאמֶר יהוה אֶל הַשָּׂטָן יִגְעַר יהוה בְּךָ הַשָּׂטָן וְיִגְעַר יהוה בְּךָ הַבֹּחֵר בִּירוּשָׁלִָם הֲלוֹא זֶה אוּד מֻצָּל מֵאֵשׁ
A similar phrase occurs in Amos 4:11 where Yahveh says that Israel was "like a brand plucked from the burning" (כְּאוּד מֻצָּל מִשְּׂרֵפָה). "Burning" (שְׂרֵפָה) is evidently related to "fire" (אֵשׁ), since the former is produced by the latter (cp. Isa. 64:11).
Gesenius (p. 20) wrote that the noun אוּד referred to "a wooden poker, so called from the fire being stirred with it." Supposedly אוּד is related to an unused verb אוּד which means "to bend, to inflect; hence, to turn, turn over" (ibid).
Thus, the idea is that the noun אוּד is something one uses to turn things over that are baking/ burning in a fire. The noun אוּד occurs three times in the Tanakh:
The LXX translates each occurrence by a declension of the noun δαλός, meaning "a firebrand."
Jastrow (p. 22) notes that אוּד also occurs in tractate Beitzah 33a (English | Hebrew) (cp. Shabb. 143a; English | Hebrew). In this particular context, the אוּד can be taken out of a "wood shed" (בית העצים), which implies that the אוּד itself is wooden. In addition, the אוּד may be broken (נשבר) and set on fire (used as fuel) (להסיק). The context seems to confirm that אוּד is a wooden instrument.
In the context of Zec. 3:2, the fire represents Yahveh's wrath and judgment. Compare:
At the time the prophet Zechariah prophesied, Israel (or, more specifically, the Kingdom of Judah, to whom Zechariah prophesied; cp. Zec. 1:12) was in captivity/ exile in Babylon. Exile/ captivity was considered a punishment/ curse imposed upon the people for disobedience (cp. Deu. 29:28). It was used in order to prompt Israel towards repentance (cp. Amos 4:11: "but you have not returned to Me").
While Yahveh's anger was kindled against His people (Isa. 5:25), the adversary (whether the angelic Satan himself, or a human adversary) stood to accuse Israel. However, Yahveh rebukes Satan, for Yahveh had chosen Jerusalem (Israel).
Jerusalem (i.e., Yahveh's people) is a wooden firebrand, a people punished but never entirely consumed by their punishment. Rather, they are rescued and spared by Yahveh Himself. The purpose of the punishment is to provoke His people to repentance.