Why does such a minor word, "the," need a whole article to explain? Because it is the most often untranslated word in Jesus's word. It is also possibly the most commonly mistranslated Greek word. In looking at an English translation of the Bible, the article "the" in the translation does not mean Greek article appears in the original Greek. And, perhaps even more often, the lack of a definite article doesn't mean that there was no "the" in the Greek. There are important instances where Greek and English usage reverses the roles of the article. For example, with the words "God" and "Lord".
The Greek Article
The ancient Greek article has a lot of different forms (o, e, to, oi, ta, tou, tes, te, ton, ten, oi, tois, tous, tais, tas, etc.) because its form changes dramatically with the number, gender, and case of the word. Many of these forms overlap with Greek pronouns, especially demonstrative pronouns. The words are or could be the English definite article "the", but many times "this" works better depending on context. The Greek article "the" is more definite than "the" in English. The Greek article is really a weaker form of a demonstrative pronoun, as in "this" or "that" and "these" or "those".
Like demonstrative pronouns, the Greek article is used as a pronoun when it stands alone without a noun. "This" is usually translated as "the one" or, "the ones" but it can also have the sense of referring to a previously mentioned noun, like any pronoun, as in "this" or "this one", referring back to the previous noun.
Like the English definite article, the Greek article can transform an adjective into a noun, for example, "strong" into "the strong," but it can also transform various verb forms and adverb words into nouns as well.
When preceding a verbal adjective, a participle, it also creates an noun, "sowing" becomes "the one sowing." When it precedes an infinitive of the verb, it creates a noun describing the action, "to sow" and becomes "the sower." In English we use the gerund, not the infinitive for this same purpose. A gerund is a verb form that ends in -ing. A gerund phrase includes the gerund, plus any modifiers and complements. Gerunds and gerund phrases always function as nouns. They can act as subjects, direct objects, indirect objects, predicate nominatives, or objects of a preposition in a sentence.
The Most Common Untranslated Articles
The most common untranslated article is in a possessive phrase. The phrase "the name of his" is translated as "his name." However, the Greek phrase putting the possessive pronoun before the noun as we do saying "his name" works perfectly well. In Greek, as in English, there are possessive forms that precede the noun without an article. Jesus, however, habitually uses the "the xxx of his" phrasing. There are several reason why he prefers the more complicated form.
This demonstrative nature of the article is especially important in this construction. In a possessive phrases, "the name of his" "the name of mine" sounds much more natural in English to say "that name of his" or "this name of mine". The noun is more emphasized by the article preceding it. Also, we must remember that Jesus love to use the final words in a phrase as a "punchline" (see this article) so the "mine" is emphasized as well.
Greek can also have constructions that has both the article and the possessive pronoun before the noun, so it is literally, "the my name." Jesus also uses this construction and it too is usually translated as "my name." However, again Jesus uses this construction for a reason. It should be translated as "this, my name." At least, if we assume that Jesus chose his words and phrases with a purpose.
The Most Misleading Untranslated Article
However, in Biblical translation into English, we commonly see the Greek article left out or translated as an indefinite article. For example, in the phrase always translated as "the son of man" is actually the phrase "the son of the man" or "this son of this man." This is especially important because the phrase "the man" has a specific meaning in Greek as it does in English. It means something like "the main man." More about this phrase in this article.
Another place where the article is almost always left off is with the word translated as "heaven." This Greek word actually means "sky" and often "skies," since the plural word appears often, but it is usually translated as "heaven" in the singular. Phrases that should be translated as "in the skies" and "of the skies" and so on. These are almost always translated as "in heaven" and "of heaven." Both the article and the plural form is eliminated. More about the "sky" phrase in this article.
Another such strategic elimination of a Greek article is in the Greek phrase translated as "the Holy Spirit." In Greek, the actual phrase is "the spirit, the holy." Since the last word is an adjective, the sense is "the spirit, the one holy." However, this does not appear to be a name or title. So the article before the adjective is ignored so that the words can be legitimately translated as "the Holy Spirit (see this article on this phrase.)
You may notice that these three non-translations are based on dogma. For religious reasons, translators wanted to think of Jesus as the son of all humanity not a "main man." Recognizing multiple "heavens" as separate from "the heaven" just doesn't work according to mainstream Christian interpretation. I am not going to note here places where such changes are made with the seeming intention of shifting the meaning to a particular point of view because the general assumption is that all translations of the Bible are made in good faith, but they are not accurate translation.
The English Indefinite Article and the Added Definite Article
Greek has no indefinite article like English does. This means that there is no phrase "a man" - just the word "man" standing alone. This may seem odd at first, but there is no indefinite article for plural words in English either. We just say, "men" like the ancient Greeks did.
However, in translating the Greek of the Bible "the's" are frequently added when no definite article is written in the Greek. Is this justified? The thinking is that if the noun refers to a specific person rather than a generic person, a "the" should be added. However, how can we tell? How do we know we aren't changing a generic statement about any man into a specific statement about a given person? The reason given is usually "the context". In looking at the Greek and at changes of this nature, it is usually impossible to see how the context dictated such a change. At least, not when we focus on Christ's words. The focus of the study here is very narrow.
Some Important Special Cases
A couple of good illustrations of the differences between Greek and English use of articles in the NT are provided by the words "God" and "Lord". In English, we do not use the article with the word when referring to the Supreme Being. However, in NT Greek, the article is always used, o Theos, "the God" or "the Divine," not theos, which would mean "a god". This means that "God" is treated as a title in Greek but a proper name in English.
However, the Greek and English word for "Lord" works differently. The Greek word, Kyrios, without an article, is used to refer to God. However, when referring to Jesus as "Lord" or "Master", the word is usually used with an article, "the master". In English, we use the title, "the Lord" in the New Testament to refer to Jesus as the Supreme Being.
However, the Greek article can also appear before a proper name, even when it is not a title. For example, the name of King David may appears as "the David." Again, to understand how this works, we have to see the Greek article more like a demonstrative pronoun, "this David" or a form of emphasis, "the David" separating King David from other Davids.