Well, very roughly (and I mean very, very roughly), articles are adjectives. Unlike regular adjectives, however, which can be omitted, articles must always come with a noun (either before, as a separate word, or after, as a suffix, in some languages). This includes zero articles, in phrases like, “[-] People need [-] food to survive.” Here, the “[-]” indicates the zero article.
Now, in most languages that use articles (including English), two types of articles exist: indefinite and definite. The English indefinite article an (or a) derives from the meaning of “one.” In fact, the words “an” and “one” stem from the same root, but we tend to drop the -n before consonants. The definite article the derives from the demonstrative that. So, your assumption that “the” implies uniqueness is a little bit off. It, in fact, implies specificity, which may or may not imply uniqueness.
Give me an apple = give me one apple (any apple).
Give me the apple = give me that apple (the apple you and I both know about, a particular apple).
The second example only implies that both the speaker and the addressee know which apple is involved. Whether it’s a unique apple (the only apple in the universe) is irrelevant.
“I think English is an irrational language. . . . But I am always trying to find logical connection between grammar rules.”
Well, let me tell you where you mistake is. Grammar rules do not determine a language; they describe it. Grammarians study languages and try to systematize their features in a meaningful, structured manner. The reason you see English is an irrational language is because you’re looking at it from the wrong end, so to speak. It’s not that English neglects the rules set for it by grammarians and tries to misbehave. It’s just that you don’t know every rule of the English language and try to make it fit the few that you do know.
If you don’t know the rules of, say, basketball, you’ll think that it’s a very “irrational” game. For example, you may think that there are too many players and too few balls, or that simply carrying the ball in the hands is much easier than bouncing it, or that by lowering the height of the hoop will facilitate easier scoring.