WordNet sense 1 (the cognitive condition of someone who understands):

apprehension, savvy, understanding

WordNet sense 2 (delicate discrimination (especially of aesthetic values)):

appreciation, perceptiveness, taste

WordNet sense 3 (the mental ability to understand and discriminate between relations):

judgment, judgement, sagacity, sagaciousness

WordNet sense 4 (the trait of judging wisely and objectively):

discretion