I'll complete your sentences to make my explanation a little easier :) 1. I could not understand why she wanted to study English 2. I could not understand why she would have wanted to study English. In the first there is no doubt in the speakers mind that she wanted to study English. The speaker is certain she wanted to study English. In the second the speaker is not absolutely certain that she wanted to study English. The speaker *thinks* she does but the speaker is not 100% certain of this as he/she is with the first sentence.

I got your point but according to the condition, the person had done something before I said. And that is why I feel confused about the sentences. Anyway thank you very much :))

I think, that it is just a conditional clause(second sentence). In German there is a "modi" for that - called "Konjunktiv". I think in English the first sentence expresses that the person was about to do something she wanted. The second is less strong, because the person thinks about doing this. But because I´m no native speaker I could be wrong.