There are several theories to language development in psychology. These theories range from development due to responses from caregivers to development due to cultural influences. Probably the most well-known theories are those that take into account development due to nature (what we are born with) or nurture (what we learn from our environment); however, many people tend to believe that development is a combination of both nature and nurture.
Burrus Frederic Skinner published a book called "Verbal Behavior" in 1957. In this book he described how language is developed through operant conditioning. For example, a baby accidentally makes a sound that resembles "ma." The mother responds in a way the baby likes. The baby tries to repeat the sound again because he is "rewarded" by the response. Skinner believed that this system of behaviours develops language in infants and later develops syntax (proper meanings and use of words) for toddlers and young children. In the debate on nature versus nurture, Skinner believed that nurture is responsible for language. A major flaw in this theory is that language has an infinite number of combinations of words, which makes it impossible for a child to be rewarded for each of them.
Noam Chomsky believed that the development of language in babies is innate. In the nature versus nurture debate, this theory is on the side of nature. Chomsky believed that people are born with something called a Language Acquisition Device, commonly referred to as an LAD. This device helps people learn language. The vagueness of this theory -- along with questions about location and function of the LAD -- are considered by linguists to be flaws.
Interactionist theory was developed to address the flaws that were inherent in Skinner's Behaviorist Theory and Chomsky's Nativist Theory; they are a combination of both nature and nurture. For an interactionist, the human body is suited for learning language (nature) and the experiences of a child learning the rules of language (nurture) are important.
Evolutionists believe that the development of the ability to learn language is due to evolution or natural selection. Language is important in the survival of the species and gives humans an edge. It is also believed that the survival of some species -- Neanderthals, for example -- may have been more successful if they were better able to communicate.
Cultural theories of language development are more about how we think due to the language we speak rather than actual language development. This hypothesis is called linguistic relativity. In the past, a classic example of linguistic relativity was the difference in perception between English speakers and Eskimos for the word snow. The theory stated that English speakers only have one word for snow and Eskimos have many words for snow because it is a dominant feature of their environment. The "Snow" theory was found to be incorrect, but it is still a great example of how linguistic relativity works.