A knowledge component is a description of a mental structure or process that a learner uses, alone or in combination with other knowledge components, to accomplish steps in a task or a problem. A knowledge component is a generalization of everyday terms like concept, principle, fact, or skill, and cognitive science terms like schema, production rule, misconception, or facet. When we say a student "has" a knowledge component, it might mean the student can describe it in words (e.g., "Vertical angles are congruent") or it might simply mean that student behaves as described by the knowledge component, but may not be able to describe it themselves. In this second case, to say the student "has" the knowledge component "If angle A and B are vertical angles and angle A is X degrees, then angle B is X degrees" means the student will behave in accord even though they might not be able to state the rule. The first is an "explicit" knowledge component, like a fact or principle, and the second an "implicit" knowledge component , like a skill. Much of what first language learners know about their first language involves implicit knowledge components.
A knowledge component (KC) relates features to a response where both the features and response(s) can be either external, in the world, like cues in a stimulus and a motor response or internal, in the mind, like inferred features and a new goal.
KCs are "correct" when all of the features are relevant to making the response and none of them are irrelevant. In geometry, for example, the knowledge component "if angles look equal, then conclude they are equal" is incorrect because it includes an irrelevant feature "angles look equal" and is missing a relevant feature like "the angles are at the base of isosceles triangle". See also feature validity and refinement.
An example of a knowledge component analysis can be found in the description of Julie Booth's study knowledge component construction vs. recall.
For further discussion and examples see:
1) VanLehn, K. (2006). The behavior of tutoring systems. International Journal of Artificial Intelligence in Education, 16 (3), 227-265 Abstract&PDF
2) Koedinger's PSLC Lunch Talk from August, 2006.
3) Norma Chang's CMU Psychology PhD Thesis (2006) on surface vs. structural probem variations and resultant acquisition of relevant vs. irrelevant features ("spurious correlations" with surface features).