In 1880, Mark Twain wrote his essay “The Awful German Language,” which is a very funny read. It is also funny from a German perspective because he is frustrated with grammatical gender in particular and gets it completely wrong, which is understandable if your native language is English. Or he got it right and could not resist the temptation to exploit if for satirical purposes.
First off, grammatical gender is not something the Germans made up, but something that the English language forgot about for the most part. Old English had grammatical gender, too, and it worked practically like in German. Actually, English is the odd man out here among Indo-European languages, along with a few others like modern Persian or Bengali.
Almost all of the other Indo-European languages have grammatical gender, and the old ones, like Latin, Ancient Greek, Old Church Slavonic, Sanskrit or Old Persian, had three grammatical genders like German: masculine, feminine, and neuter. Some lost one of the three along the way. Danish and Swedish (but not in all dialects and not in Norwegian) conflated masculine and feminine into one common gender. Dutch mostly did the same, but again not in all dialects. The Romance languages and most of the Indian languages merged neuter into masculine instead.
Originally, the Indo-European language seem to have had a different classification for nouns: animate and inanimate. Armenian and the Slavic languages still have remnants of this, but most other languages in the group have long lost it. Later the animate category apparently split into masculine and feminine which for animate nouns would correspond to male and female.
However, since words looked similar for both animate and inanimate nouns and were declined in the same way, the masculine and feminine categories expanded into the latter although that made no sense as a classification for male and female. Mostly the form of a word determined this. And then it could work also backwards, and words where a distinction between male and female could make sense got a different grammatical gender assigned.
For example, German “Mädchen” (girl) is a diminuitive with “-chen” (like English “-let”) from “Magd” (a female domestic worker, like English “maid”). But all such words are neuter because of their ending. And so a girl is neuter in German, which is, of course, weird if you take it literally. Collective nouns ending in “-schaft” (like English “-ship”) are feminine because of their form. So the German national soccer team is “die Mannschaft” (feminine, also for the men’s team). Some words were imported from the Romance languages like “Person” or “Figure” (eg. in a play) and kept their original feminine gender although they may also refer to a man.
But there is also a funny example in English: The original words in Old English for “man” and “woman” were “wēr” (like Latin “vir”) and “wīf” (like modern “wife” and German “Weib,” which used to be neutral, but now is pejorative). The former was masculine, and the latter neuter. There was also a word for a human being in general: “mann” which was masculine. Since “wīf” could also mean “wife,” to make clear what you meant, you could use “wīfmann” for a female human being (like Japanese: “onna no hito”).
Now under the influence of Norman this changed. In the Romance languages “man” and “human being” are the same word, derived from Latin “homo.” The English followed this example and started to use “mann” for men and humans in general. That’s why English had to come up with an awkward “human being” later, whereas German has the handy “Mensch.” The word “wīf” drifted more in the direction of “wife.” So the word “wīfmann” became the standard word and evolved into “woman,” which is, strictly speaking, masculine because the latter part “mann” determines the grammatical gender.
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What you basically have with grammatical gender is three different classes for nouns, where the distinction between masculine and feminine sometimes coincides with that for male and female, but mostly doesn’t. Hence, if you are confronted with a word in German that is masculine it does not make sense to think of maleness in the first place, the same for a feminine word and femaleness. You really have to concentrate on this to make such a connection, which is not automatic and mostly nonsense. You could have a spoon (masculine), a fork (feminine), and a knife (neuter) in front of you, but would be hard pressed to associate them with maleness, femaleness, or whatever.
When Mark Twain translates from German to English, though, grammatical genders suddenly take on a very concrete sense that it does not have in German. And that is, of course, hilarious. If your native language is English, you simply can’t get the point of grammatical gender. One funny example I often see is when people write that a woman has “blonde hair,” but a man has “blond hair.” The word comes from the French, and the first form is feminine, the second masculine. But this is determined by the word “hair,” which is masculine in French, and neuter in German, not by whether it is a woman or a man!
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So what is the advantage of having three classes of nouns? First, there is clearly a disadvantage: You have to learn which is which, and I understand why Mark Twain was so frustrated with it. But that is not a problem if you learn the language as a child where it is like inhaling air. And then there are also some implicit rules behind this that have a certain logic, though there are also many exceptions. The form of a noun often determines its grammatical gender. Hence it is not as random as if someone had just rolled the dice.
The advantage is that in a given context, there are words that are in the different categories. You can then refer to them by their grammatical gender and that can remove ambiguities. For example, if you have a spoon, a fork, and a knife in front of you and you want to pick one, in English you can only say: “I take it.” Totally unclear what you mean.
In German you can say: “ich nehme ihn/sie/es” depending on whether you mean the spoon, the fork, or the knife, and there is no ambiguity. Of course, since grammatical gender is rather random, also in German it doesn’t have to be as clear-cut. There could be two things in a context that are masculine, feminine, or neuter. Then you also have to work harder, but often you don’t.
It is even more useful in a complicated sentence where in English you can only speak of the “silver one,” for example. Is this the spoon, the fork, or the knife? In German, you can make it clear with: “der silberne” (masculine), “die silberne” (feminine), or “das silberne” (neuter). You also don’t need the “one” because the material is “Silber” and the adjective “silbern.”
And it can also be practical in a complicated sentence if you want to refer to something with a subordinate clause. In English, it can only be “that” or “which,” whereas in German you can use “welcher,” “welche,” or “welches” depending on the grammatical gender. I guess that is also one reason why you can build monster sentences in German. And it may make it difficult to translate them from the German because you introduce an ambiguity that was not there before. English often has to repeat the noun for clarity, something that is scorned at in German style.
Some languages have gone even further than the Indo-European languages. The Bantu languages have about twenty different categories for nouns, eg. for humans, animals, plants, liquids, or abstract concepts. That is in principle similar to grammatical gender, only more logical. In Chinese, and influenced by it also in other languages like Japanese, things are assigned to dozens of different classes for counting. You make clear whether you are counting “objects with a protruding top” like hats or “wheeled vehicles” like cars. That removes ambiguities. But then I would also guess that the Count von Count will have a more demanding task teaching children the numbers.
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All in all, grammatical gender has some uses and it is not what it may seem to those with English as a native language like Mark Twain. It is not that you think of masculine or feminine nouns as in some mystical way male or female. You really have to concentrate on that and then it is just as funny as it sounds in English.