Ah.. Moe...
Both Anime Network and Wikipedia's Definition,
But Moe... its kind of hard to explain, it depends how you see it as. There are actually a lot of different meanings of Moe.
Anime Network:
Moe is a Japanese term used in connection with manga or anime to describe something precious, usually (but not always) the ideal of youthful and innocent femininity. Written with the kanji for "to bud or sprout" (萌), the concept covers a range of ideal behaviour for youthful female characters in manga or anime. To be moe, a character can be eager or perky, not overly independent, and call forth a desire in the viewer to protect them and nurture them. The term is also used to describe any preciously cute item; there is an animal mascot character store in Tokyo called Moe.
Wiki:
Moe (萌え?, pronounced [mo.e], literally "budding", as with a plant) is a Japanese slang word originally referring to a strong interest in particular types of character in video games or anime and manga. For example, 眼鏡っ娘萌え, meganekko-moe, "glasses-girl moe", describes a person who is attracted to fictional characters with eyeglasses. "Moe!" is also used within anime fandom as an interjection referring to a character the speaker considers to be a moekko. It is even used in some anime, such as Ouran High School Host Club, Ai Kora, Lucky Star, Kaichou-wa Maid-sama!, The Melancholy Of Haruhi Suzumiya and K-ON. There are various interpretations of what moe is today. Joseph L. Dela Pena argues that moe is a pure, protective feeling towards a character[1],