First and foremost, interacting with your child almost as an equal- intellectually, not behaviorally- encourages them to act more mature. This not only encourages brain growth, but will also help them understand the people in the world around them are not there to baby and cuddle them. They will be more inclined to understand problem solving and the concept of being proactive.
Namely, reading to your child is crucial to their intellectual development. For obvious reasons, this is great for their communication skills. Children who are read to show much stronger vocabulary and are much more confident in daily interactions typically required of successful people. Language skills in our society make for the building blocks of confidence in scholastics and the workforce.
Also socializing your child is important to their social development. Playing with peers helps children understand how individuals interact and how they react to certain scenarios and attitudes. Socially stunted adults were more often than not children with very limited interactions as children, when their social queues were still impressionable.
Every parent present in their child’s life wants to watch them grow into intelligent, accomplished people with a better life than their own. Even showing intention for encouraging intellect in your child’s life already gives them a leg up on children with parents who couldn’t care less. Intellectually-developed children lead much more fulfilling lives and maintain much more successful careers.