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.