理解 & 了解
-Are you clear? ( 你理解了吗?) -Yes, I am.(是的。)
-Do you understand? (你了解了/明白了吗?) -Yes, I do. (是的。)
“理解” expresses you have understood completely . You have known why he does something like that, moreover, you can predict what is his next step.
“了解”conveys you just have known he does something. You are negative to receive some information.
e.g.: Jack told you sb has cheated you, you received this information, you can say “我了解了。(我了解这件事本身或是这个人了。)”While, if you knew the reason why he cheated you, (may be he needed money urgently) you can say "我理解他。”
I hope it can help you.