A judgment is analytic when it contains nothing but an elucidation of what is already thought through one of its concepts. For example, in the judgment All bodies are extended, the concept body is elucidated by exhibiting the concept extended, which is already thought, though perhaps not explicitly, when thinking of body. (This characterization of analytic judgments opens Kant to the charge of “psychologism.”)
For I do not need to go beyond the word body in order to find that extension is connected with it. All I need to do in order to find this predicate in the concept is to dissect the concept, i.e., become conscious of the manifold that I always think in it. (A7/B11)
Kant frames his official account of analytic judgments in terms of categorical subject-predicate judgments (which may be either affirmative or negative). Thus the predicate is already thought through the subject in an affirmative analytic judgment.
The criterion of the truth or falsehood of an affirmative analytic judgment is the principle of contradiction, which states that “No thing can have a predicate that contradicts it” (A151/B190). To claim that bodies are unextended would predicate of the concept body a predicate which is contradictory to it. So if the denial of an analytic judgment implies a contradiction, the judgment is true.
Analytic judgments are all a priori; that is, they may be validly made without any reference to experience. All that is needed to determine their truth is the dissection of concepts.
Analytic judgments are contrasted with synthetic judgments, which are ampliative, rather than explicative. In the synthetic judgment, a predicate which is not contained in the subject itself is joined to the subject.