Luke 24:47 And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.
And to be a herald by that name of his, a change of minds in regards to letting go of mistakes into all ethnic groups beginning out of Jerusalem.
This is a great example of Jesus's word being changed from their original meaning into more religious terms that would not have been understood in his era. The verse is also rearranged to emphasize those terms. There verb makes it clear that this verse is actually a continuation of the previous statement. The verb is changed and a word is added to make it sound like a paraphrase rather than a direct statement, continuing the last.
The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").
There is no Greek word "that" here. It is added to make this sound like a paraphrase following a direct quote. However, if the previous verse is read as a direct quote, this one should be to since it continues that statement.
The verb translated as "should be preached" appears here in the Greek, which is important because it continues the string of infinitives ("to suffer," "to rise") in that verse.
"Repentance," is the uncommon noun form of a very common verb. It means "a change of mind or heart", "repentance", "regret", "afterthought", and "correction". In English, this idea is can be expressed as "hindsight". It is from a verb that means "to perceive afterward". Though in the form of an object, this word is not exactly the object of the verb "preach" because that word is passive (see below).
There is no "and" here. Instead there is a preposition that means The word means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure. The meaning here is clearly "in regards to".
"Remission" is from an uncommon noun form of the word Jesus often uses that is translated as "forgive" but which means "let go" or "let drop." Its sense is "release" as in releasing something so it is free. Elsewhere in Luke this word is translated as "liberty". "Letting go" captures the idea well.
The word translated as "sins" is a form of a word that means "to fail in one's purpose", "to neglect," and "to be deprived of." It has no sense of doing malicious evil in Greek. The best English translation is "mistakes" or "failures" rather than what we commonly think of as the evils of "sin." See this article for more information and context.
The word translated as "should be preached" means "to act as a herald", "to proclaim," and "to declare." It is not an active verb, but an infinitive, the third infinitive of the sentence, the first two were in the previous verse. The form is passive so "to be a herald" is the direct meaning.
The word translated as "in" means "on", "over", "upon", "against", "before", "after", "during", "by" or "on."
The word translated as "his" is the Greek word commonly translated as third-person pronouns in English. If this is a paraphrase, it would seem to refer to Jesus, but if it was a direct statement, it would refer to the Father.
The Greek word translated as "name" is much more complicated than it might at first appear. It can simply mean a "name" as in English, this can be many things. It doesn't mean the thing itself, but what people call it. For example, it can mean a "false name," or "a pretense" as we say "this is a marriage in name only." It can also mean representing another person's authority, as we say, "he is acting in the name of the boss."
The word translated as "among" means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure.
The word translated as "all" is the Greek adjective meaning "all", "the whole", "every," and similar ideas. When it is used as a noun, we would say "everything." As an adverb, it means "in every way", "on every side," and "altogether."
The word translated as "nations" is usually translated as "gentiles" but it means "a group of people living together," a nation, a tribe, or a cast of people. Later it came to mean "barbarous nations" similar to our idea of ethnic people. It is in the same form as the "them" above, so "to them" or "for them." It is the Greek word from which we get our word "ethnic".
"Beginning" is from a verb in the form of an adjective that means "to be first", "to begin," and "to make a beginning", "to rule", "to govern," and "to command." The two meanings, "to start" and "to command" create different meanings when paired with the following verbs. The form is that of an adjective, "beginning" or "starting".
The word translated as "at" means "from" in both location and when referring to a source. It does not mean "at".
The word "Jerusalem" denotes the city or its inhabitants. Two different forms of this word appear in the NT. This is the only time this form is used in Matthew. It is only used once in Mark, but not in Christ's words. It isn't used at all in John. This version is used most heavily in Luke, mostly in his narration, but a few times in Christ's words. It seems to be the more formally Greek version of the name.
καὶ (conj/adv) "And" is kai, which is the conjunction joining phrases and clauses, "and," or "but." After words implying sameness, "as" (the same opinion as you). Used in series, joins positive with negative "Not only...but also." Also used to give emphasis, "even", "also," and "just." --
κηρυχθῆναι ( verb aor inf pass ) "Should be preached" is kerysso, which means "to be a herald", "to summon by a herald", "proclaim", "call upon", "announce", "declare," and "command publicly." Only in the NT is it translated as "preach" or "teach publicly." --
ἐπὶ (prep) "In" is epi, which means "on", "over", "upon", "at", "by", "before", "across," "after" in position, "during", and "against." --
τῷ ὀνόματι ( noun sg neut dat ) "Name" is onoma, which means "name." It means both the reputation of "fame," and "a name and nothing else," as opposed to a real person. Acting in someone's name means to act on their behalf, as their representative. --
αὐτοῦ (adj sg masc gen) "His" is autos, which means "the same," and the reflexive pronouns, "myself", "yourself", "himself", "herself", "itself," or the oblique case of the pronouns, "him", "her," and "it." It also means "one's true self," that is, "the soul" as opposed to the body and "of one's own accord." In the adverbial form, it means "just here" or "exactly there." --
μετάνοιαν [uncommon] (noun sg fem acc) "Repentance," is from metanoia, which "a change of mind or heart", "repentance", "regret", "afterthought", and "correction". In English, this idea is more precisely expressed as "hindsight". It is from a verb that means "to perceive afterward".
εἰς (prep) Untranslated is eis, which means "into (of place)," "up to (of time)", "until (of time)", "as much as (of measure or limit)", "as far as (of measure or limit)", "towards (to express relation)", "in regard to (to express relation)", "of an end or limit," and "for (of purpose or object)." --
ἄφεσιν [uncommon](noun sg fem acc) "Remission" is the noun aphesis, which means "letting go", "release", "relaxation", "exhaustion," exemption from attendance", "leave of absence", "divorce, and "the beginning [of anything]".
ἁμαρτιῶν ( noun pl neut gen ) "Sin" is hamartia, which means "to miss the mark", "failure", "fault," and "error." Only in religious uses does it become "guilt" and "sin." --
εἰς (prep) "Among" is eis, which means "into (of place)," "up to (of time)", "until (of time)", "as much as (of measure or limit)", "as far as (of measure or limit)", "towards (to express relation)", "in regard to (to express relation)", "of an end or limit," and "for (of purpose or object)." --
πάντα ( adj pl neut acc ) "All" is pas, which means "all", "the whole", "every", "anyone", "all kinds," and "anything." In the adverbial form, it means "every way", "on every side", "in every way," and "altogether." --
τὰ ἔθνὴ, ( noun pl neut acc ) "Nations" is ethnos, which means "a number of people living together", "company", "body of men," "tribe", "a people", "nation," and (later) "foreign, barbarous nations." --
— ἀρξάμενοι ( part pl aor mid masc nom ) "Beginning" is from archomai, which is a form of archô, which means "to be first", "to begin", "to make a beginning", "to rule", "to govern," and "to command." --
ἀπὸ (prep) "At" is apo, a preposition of separation which means "from" or "away from" from when referring to place or motion, "from" or "after" when referring to time, "from" as an origin or cause. --
Ἰερουσαλήμ: (Aramaic noun) "Jerusalem" is Ierousalēm, which is a form of word that denotes the city or its inhabitants. Two different forms, this form and Hierosolyma, appear in the NT. --