It’s not a simple question! Human language differs from animal and plant communication systems in that it enables the transmission of ideas, which are abstractions. Think of the Pythagorean theorem or tripartite government.

Many explanations of how human language came to exist seem to be stabbing in the dark.

Here are some of the current theories: Could language have arisen from hand gestures? We are told that “Wild chimpanzees, for example, have been seen to use at least 66 different hand signals and movements to communicate with each other. Lifting a foot towards another chimp, for example, means ‘climb on me’, while stroking their mouth can mean ‘give me the object’” (Horizon August 20, 2019). But these aren’t ideas, just requests. A variety of such theories of language have been termed the Bow wow, the Ding dong, the La la, the Pooh pooh and the Yo he Yo theory theory, gives us some idea how seriously they are taken.

There are a number of more elegantly named theories. “tabula rasa,” “behaviorism,” “universal grammar,” “acculturation,” and “monitor” theory. Philosophers add weight and significance to the question but it is less clear that they shed much light.

Part of the problem is that most common words in any language have a huge number of meanings, bandied back and forth, and sometimes failing to communicate as intended:

If words are to keep the world at arm’s length, they must also be uninvolved in what they mean – they must designate it arbitrarily. But if words fail to completely detach, that failure should tell us something about the peculiar – and humble – position we occupy ‘between gods and beasts’, as Plotinus put it.

Alexander Stern, “The way words mean” at Aeon

And yet meaning seems inexhaustible:

Human language is amazingly creative. If you make up a sentence of any complexity, and search for that exact sentence on the Internet, it’s almost never there. Virtually everything we say is novel. Yet at the heart of this capacity of ours lies an incredibly simple piece of mental technology: Merge. Merge takes two bits of language, say two words, and creates out of them another bit of language. It builds the hierarchical structures of language.

David Adger, “This simple structure unites all human languages” at Nautilus

Some think language might have “hijacked” our early ancestors’ brains, as if it were a person of some kind:

Kolodny points out what might seem like a contradiction in this notion: Many species of ape use tools in sequence-dependent ways and also have highly developed levels of communication. But the order in which those apes produce their utterances doesn’t make much difference to their meaning, Kolodny explains. “The question becomes not ‘How did language arise only in humans?’ but ‘Why did it not arise in other apes as well?’ And the answer is, the qualitative difference between us and other apes is they don’t have the communication system coupled to those temporal sequencing structural capabilities.”

Ben James, “A Sneaky Theory of Where Language Came From” at The Atlantic

Well, the only thing that’s obvious is that the apes don’t have language. And that we have it, for better or worse.

Further reading:

The real reason why only human beings speak. Language is a tool for abstract thinking—a necessary tool for abstraction—and humans are the only animals who think abstractly

and

Can we talk? Language as the business end of consciousness