The origins of language have been speculated on since antiquity. Many myths tackle language, like the Tower of Babel for example. Others say that their gods endowed them with language too. Later on, people tried to see what the first language was by doing an experiment. One such experiment was to raise a child without language and see what utterances it made.
History contains a number of anecdotes about people who attempted to discover the origin of language by experiment. The first such tale was told by Herodotus(Histories 2.2). He relates that Pharaoh Psammetichus (probably Psammetichus I, 7th century BC) had two children raised by a shepherd, with the instructions that no one should speak to them, but that the shepherd should feed and care for them while listening to determine their first words. When one of the children cried “bekos” with outstretched arms the shepherd concluded that the word was Phrygian because that was the sound of the Phrygian word for bread. From this, Psammetichus concluded that the first language was Phrygian. King James V of Scotland is said to have tried a similar experiment: his children were supposed to have spokenHebrew. Both the medieval monarch Frederick II and Akbar are said to have tried similar experiments; the children involved in these experiments did not speak. (Wikipedia)
Today, anthropologists and archaeologists have come up with many different theories on why humans evolved language. The most prevalent one is that as human societies became more complex, they needed more ways to communicate with each other beyond body language and grunts. Organizing strategic complex activities like hunting with a group and finding the best way to attack another settlement for example, need a complex thing like language to plan it all precisely. Some say that language is part of human symbolic culture as a whole. Abstract thinking developed in more later hominids and language needs abstract thinking to work, as words are symbolic of what they represent. One has to equate words with things or concepts as words themselves are meaningless without an interpretation. They say that language developed when humans evolved more abstract thinking skills. The origins of language are probably a mixture of those factors and many more included in other theories. There’s probably no one-way language evolved.