懂: to understand (the meaning of something) 懂得 is more or less the same but more "formal"; e.g. to understand a concept
了解: to know something well, as opposed to 知道 : to have a "lot" of informations about somthing or someone. That's the word you use to say you know someone well. So has a deeper meaning than 知道
理解: same as 了解, but you also understand "why" or "how". For example you understand why your friend acted in a specific way, or you understand someone's motives, 我理解他。 You can also 理解 how to use the word 理解. 懂得 is close to this meaning.
明白 kind of means that you were confused before and everything is clear now. if you look at the litteral meaning of the word 明 白 : it's like you become enlightened and everything becomes crystal clear.
(more)了解: to know something well, as opposed to 知道 : to have a "lot" of informations about somthing or someone. That's the word you use to say you know someone well. So has a deeper meaning than 知道
理解: same as 了解, but you also understand "why" or "how". For example you understand why your friend acted in a specific way, or you understand someone's motives, 我理解他。 You can also 理解 how to use the word 理解. 懂得 is close to this meaning.
明白 kind of means that you were confused before and everything is clear now. if you look at the litteral meaning of the word 明 白 : it's like you become enlightened and everything becomes crystal clear.