@luolin,

了解 is to understand or to know some background information or knowledge. For example, 我和这个人是老朋友，我很了解他.

知道 is very similar to 了解. However, if you say 我知道这个人, it means you know this guy (but don't know very well) or you have heard of this guy or maybe you have only said hello to each other once, but you have an impression of this person. So you can say 我知道这个人，但是我不了解他.

明白 is very much like 理解. However 理解 is more like to understand someone's feeling or thoughts, while 明白 is to understand some 道理 or facts.

--Echo

echo@popupchinese.com