Speech is perhaps what makes us different from apes. They can have some degree of logics, but this is boosted to astronomic values in humans by speech. Speech is made of two sets of symbols: words and grammar, rules through which words are combined in phrases expressing precise links between objects and events. "John hit Paul" has a different meaning from "Paul hit John". Words may be the same, but grammar changes the meaning.
Crying is the first sonic message of the infant, resembling more animal communication than human speech. Mothers can make after a time the difference between hunger, rage or pain cries, by using clues at the beginning. Researches showed that if a mother is receptive to the manifestations of her infant, reacting rapidly and regularly to its crying, the infant cries less till the age of one year, compared to the children of mothers reacting differently. Besides crying less, infants communicate better through gestures and sounds. By the age of 4-5 months, most babies start making sounds repeated regularly as vocal actions called babbling. Till the age of 18 months, "speech" is still mainly a play or an accessory of different actions, not a substitute of them. The communication need is satisfied through gestures and expressive noises "language". The child-parent communication is possible because the parent has learned to associate specific calls and gestures to certain needs. This communication allows the infant to make its requirements well understood.
Infants seem to differentiate between speech and other sounds, like adults do. If a 1-or-2-month-old infant is taught to suckle from the nipple by hearing specific sounds, like "a-a", it will finely stop doing it because it gets bored by the same sounds; once it has got a memory model of the sound, this is not new and interesting anymore. Changing the "a" sound with another vowel (like "e-e-e") will make the infant suckle further; it distinguishes the difference and turns interested again.
Infants behave differently with objects and people. It looks carefully at objects and tries to get to them, but with people it will attempt to speak from an early age. When in visual contact with the parents, the child makes a lot of body and face gestures, resembling those of the adults in their conversations, and can make some "pre-speech" movements with the lips; it's like the child would talk before being able to do it. At the beginning, the parent may be imitating the child, this being one of the ways the child learns social meaning of various gestures that it displays automatically.
Even if learning capacities of the child seem limited, it learns the complex structure of its mother tongue in just 3-4 years. Even if facing various language patterns and learning little or unconsciously from the parents, the child will reach their grammar level in a short period of time.
First, the child pronounces isolated words, usually a noun indicating a person or object. These words would transmit ideas, which adults express through phrases. "Milk", for example, can mean "I want to drink milk".
Soon, the child starts joining two words, including verbs. These phrases describe connections between people, objects, actions and events, like "daddy hurt" or "kick ball". The words are used always in concordance with the grammar order used by the adults, a first sign of grammar learning. The child will say "kick ball", but rarely "ball kick".
During the telegraphic phase, all words and terminations subtly modifying the meaning lack. Numbers (and plural formation), times (other than present time), precise objects and locations are omitted. While an adults says "The book is on the table", the toddler says "book table".
Till the age of 18 months, infants learn to decode the adult speech. Then, they learn vocabulary and some arrangement rules, necessary to understand speech. The child keeps on forming longer phrases, by adding omitted speech parts during the telegraphic phases. By the age of 4-5, the child can maintain conversations like those between adults.
Many brain areas are involved in this development. The cortex and cerebellum are involved in transmitting the right commands to the lips and tongue. Other two important brain areas are Wernicke's nucleus and Broca's nucleus. Wernicke's area, in the temporal lobe, decodes the meaning of the sounds and transmits signals to the Broca's area, in the frontal lobe. Broca's area generates all the motor commands, necessary for the contraction of the muscles involved in speech. In right handed people, speech areas are located in the left hemisphere. In the left handed persons, speech is usually located in the left hemisphere, but in 15 % of the cases in the right hemisphere, and in 15 % of the cases in both hemispheres.
Chimps grown in human environments understand speech, not only individual words, but also simple telegraphic speech. But that's all. They cannot use their lips and tongue like humans do in order to pronounce words, but they can learn sign language and understand the use of verbs and nouns.