My understanding is that 理解する is more like comprehension. 「この問題を理解するのは難しい。」　－　This question is hard to comprehend. Or, this question is difficult to make out. Whereas わかる　（There are different kanji forms of wakaru, it is best to just use hiragana, I think. That's what I see most often) is a broader term of understanding　or knowing. I hear it much more often. 「わかりますか。」　「はい、わかります。」 Do you understand? Yes, I understand. This website http://tatoeba.fsffrance.org/eng/home is great for finding sentences with vocabulary.

Hola Augustin, I agree with Alicia's comment. I would like to add a little bit more. わかる and 理解する　are used as synonymous and the meaning is almost equal but sometimes the nuance is slightly different depending on the context. Usually we use わかる　in hiragana. わかる is translated "to know, to understand" in English. However this word also includes the connotation of はっきりする(to be clear)、判断（はんだん）する (to judge) 、識別する（to recognize, to discern) and 理解する (to understand, to comprehend) etc... 理解する.......to understand or to seize what is meant correctly, precisely This is just an example. Sometimes people say like this わかってるつもりでも理解していないことが多い There are many things you don't understand even though you feel you know them. I hope this helps.

I agree with Alicia's comment. 分かる can be also used as "know"; therefore it may have a lighter impression depending on the context. For example, 今日、本当に暑いよね。(Today is really hot, isn't it?) うん、分かる--!!! (Yeah, I know--!!!)