Best explanation I ever saw was in a conversation between an American and a Japanese on a discussion board somewhere. American admitted that he found it difficult to quantify exactly why he liked a character, but that “it was like she’d found a little place in his heart”, and he figured that was what moe was. Japanese guy replied that he understood moe exactly.

Think of it like cuteness, in that there is room for individuals to say “this is cute” even when you absolutely disagree (think goths), but at the same time there’s a rough consensus for what constitutes cute for most people. That’s how moe works - you can have your own, but there’s also a sort of average otaku moe.