
Originally Posted by
iCake
That's basic grammar there. Нравиться doesn't mean "to like", but rather "to be likable". That's where "мне" comes in, as it's not "I like it" but "it's likable to me".
As for the pronouns я, ты etc. with this word. You use it for what actually is an object of "like" in the English sentence:
I like her - Она нравится мне.
As you can see "I" turned into "me - мне in Russian" and her turned into "she - она in Russian".
This is not because Russian is so weird, it's because "нравиться" and "like" have a different semantic meaning.