American Heritage Dictionary defines "cognition," from which "cognitive" is derived (i.e., that which relates to cognition), as:

1. The mental process of knowing, including aspects such as awareness, perception, reasoning, and judgment, and 2. that which comes to be known, as through perception, reasoning, or intuition; knowledge.

So when asking about "cognitive development theory," you're asking about the scientifically developed and tested ideas (i.e., theories) about how the thinking, perception, intuitive, awareness, reasoning, judgement, and knowledge portions of your brain and experience develop over time from babyhood to adulthood--and how they continue to change (for better or worse) in adulthood.

Cognitive development theory was a reaction against Watson and Skinner who believed babies were born with no capacities and so didn't "develop" but only "learned." Cognitive development theory says, in brief, that humans are born with native cognitive qualities and abilities that grow over time at predictable but different rates and may be influenced by both heredity and environment so that an individual's perceiving and judging and reasoning and intuition etc. may be impacted a variety of different ways by both their ancestry and their living, educational, and community etc. environments.

People develop at measurable and predictable rates, and generally go through predictable stages. Some researchers have studied behavior, from babies to adults, and quantified these stages. Piaget is one such person. He designed cognitive stages of development. Erickson developed stages of moral development. The idea is that you usually go from one stage to another, in order. You don't normally skip stages (although you may spend longer in one), and once you reach adulthood you will normally remain at the stage you have reached.

The cognitive development theory is based on the idea that human beings are able to take in stimuli, perceive that stimuli, have the ability to think and thus will learn or achieve an understanding of the world around us.  This learning takes place through not only what we learn but also through our genetic make-up.  Cognitive development encompasses the act of processing information, our intelligence abilities, our ability to reason, remember and our ability to develop our memories.

Even though each person is an individual and unique, there are patterns that all humans follow.  When children are born there are specific benchmarks that a child is supposed to reach by a certain age.  These not only pertain to physical benchmarks but also include genetics and cognitive development. 

Many psychologist, scientists and educators have studied the concept of cognitive development but probably the most read and the most famous is Jean Piaget.

"The development of thought processes, including remembering, problem solving, and decision-making, from childhood through adolescence to adulthood."

Perhaps the links I have listed with this reply will give you more of the information for which you are looking. 

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