Wikipedia does pretty good at breaking down "moe", exploring all its various interpretations since many find it hard to define in one single line. But basically I consider it an attraction to someone vulnerable, innocent, or just plain cute. In most folks, it turns on protective instincts to a degree, but either way it's just generally an attraction, to a character with delicate properties that could easily be destroyed by disaster or evil. Properties which you can cherish because they are so delicate. Innocence the character may grow out of but you hope never will. It's just an appreciation of what's become a transient, rare thing: Innocence.

In what direction, and how far, people take that appreciation depends on the individual.