A cognitive reduction is a form of reductive analysis where, rather than reducing something to physical phenomena, we reduce something to the cognitive machinery which give rise to the idea.
For example, Bayesian probability (ie subjective probability, or credence) can be seen as a cognitive reduction of randomness: rather than seeking physical causes of randomness in the world, we seek the impression of randomness in the mind. We then assert that randomness exists in the map, not the territory.
In other cases, we may still think the phenomenon exists in the territory, but nonetheless seek a cognitive reduction. For example, while we may think “apples” are a real thing that exists, we might be confused about borderline cases (such as a hypothetical fruit which has 90% apple genes and 10% pear genes). A cognitive reduction of “apple” helps us understand what it even means to assert one thing or another about borderline cases, while not necessarily giving up the claim that apples are real things which exist.