It means something like "it occurs to me that....." or "an idea or a thought suddenly strikes me" in English. The subject of the verb "cae" is the subordinate clause initiated by "que", so it's in the third person singular. "Me" is in the dative case.

It is an expression or idiom. It has to be follow by some other words in order to be completed and understood. For example, "me cae que si aprender ingles" this can be translated into English by saying : "I bet you will learn spanish" Hi Andy, my name is Uri Quintal. I am an ESL and Spanish teacher graduated from the Arizona State University in Phoenix, Az. I offer some basic lessons for non-native Spanish speakers in order to help students not only to speak another language but to think and dream in another language for a very cheap price while I help them to develop their conversational skills. I can also teach you some other idioms commonly used in Spanish. Please feel free to contact me if you are interested. Have a nice day! :)