I'm familiar with the term, but to be honest, I've never really understood what it meant. I've always thought it was in relation to a fetish, and while that interpretation seems to be correct, 'moe' is a much broader term than I orginally thought.
According to wiki, the symbol for 'moe' literally means 'budding' (eg, the Japanese word for Dolphin is made up of the symbols for 'Sea' and 'Pig'), which I think may have originally stemmed from the concept of a 'Yamato Nadeshiko' (ideal woman). The meaning has altered over time, but I think the cute aspect of 'moe' remains the same.
I like this description from Urban dictionary:
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 new meaning of 'moe' is entirely caught up in issues surrounding hobbies and taste. Specifically, 'moe' means be attracted to a specific character or its specific partial element and to have a favor feeling toward it. 'Moe' suggests the condition of being infatuated with one character or thing and implies an image of someone burning with desire.
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.
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.
Okay. So an aspect of a character that I find 'moe'? I think Tsundere characters - specifically when they are embarrassed. I can't help but love an agressive, awkward character blushing madly.
