A Japanese slang term (ironically, first employed by otaku) used to refer to the fetish for or sexual attraction to idealized people, usually a fictional perfect young girl.
Since then, moé has come to be used as a general term for a hobby, mania or fetish (non-sexual or otherwise). This is contrasted with otaku, which would be taking the specific hobby, mania or fetish to harmful levels.
The picture becomes clearer when we hear the frequent use of 'moe' referring to specific elements or characteristics, such as 'weak girl moe,' 'young lady moe,' and 'glasses moe.' The meaning of 'glasses moe' refers to a taste that is taken with a character who wears glasses; furthermore, this taste fetishizes the feature itself of glasses-wearing. In this case, glasses are the 'moe' element.
Please imagine the feeling when you first liked somebody. The passion pops up inside of your brain and heart. This is not logical and unexplainable. And "moe" is a feeling very similar to this specific moment
The word cute captures an aspect of it, but cute doesn't necessarily imply moe, while moe almost always implies cute.