From Wikipedia:

“Caregivers of an infant are advised to pick up on the infant’s facial expressions and mirror them. Reproducing and empathizing with their facial expressions enables infants to experience effectiveness and to recognize their own actions more easily (see mirror neurons). Exaggeratedly reproduced facial expressions and gestures are recommended, as they are clearer forms of expression. The baby’s babbling should also be picked up and repeated. By imitating each other’s sounds the first simple dialogues are initiated. Accentuated pronunciation and melodic intonation make it easier to recognize individual words in a sentence. However, it is not advisable to use simplified “baby talk” (e.g. “Did you ‘ouch’?” instead of, “Did you hurt yourself?”).

“Even if parents cannot yet understand infants’ babbling, a timely response by parents to babbling leads to faster language acquisition. This was confirmed by researchers who first studied mothers’ behavior towards 8-month-old infants and later tested the infants’ vocabulary when they were 15 months old. A first important development of infants is the discovery that they can influence their parents through babbling (development of intentional communication). Parents can encourage this by engaging with their infants in babbling. This in turn promotes further language development, as infants then turn to their parents more often.

“Previous studies have shown that the infant’s speech is encouraged when parents, for example, smile in the infant’s direction or touch the infant every time the infant looks at them and babbles. It also helps if parents respond to what they think their baby is saying (for example, giving a ball or commenting when the baby looks at the ball and babbles). Responding to sounds produced when the baby looks at an object (object-directed vocalizations) thus provide an opportunity to learn the name of the object. In this way, babies also learn that sounds are associated with objects. However, language development is only achieved if parents react positively (e.g. smile) in response to the infant’s babbling. A high response rate without a connection to the infant’s utterances does not lead to language promotion. It is detrimental to language development if a mother instead tries to divert the infant’s attention to something else.”