noun
understanding; comprehension; realization
General non-religious use for grasping or realizing something. In modern Japanese it is often felt as a somewhat abstract or set-expression noun rather than the everyday word for ordinary understanding.
彼女は悟りが早く、一度説明すればすぐ要点をつかむ。
She is quick to understand and grasps the point as soon as it is explained once.
noun
enlightenment; spiritual awakening; satori
Buddhist and religious-philosophical use for awakening to ultimate truth; also used more broadly for a profound spiritual insight.
僧は長い修行の末に悟りを開いた。
The monk attained enlightenment after long years of ascetic practice.
彼は悟りの境地に達したと語った。
He said he had reached a state of spiritual awakening.
理解 is the ordinary, broad word for understanding information, explanations, or people; 悟り is more abstract and can suggest deep realization.
悟る is the verb meaning to realize, perceive, or become enlightened; 悟り is the corresponding noun.
解脱 is a Buddhist term for liberation from suffering or the cycle of rebirth; 悟り focuses on awakening or enlightenment.
A noun form related to the verb 悟る, meaning to realize or awaken. 悟り is the standard spelling; 覚り uses a semantically related but rare alternative kanji.