Moe (Moh-Eh) is written with the characters 萌え. It comes from the character meaning "to bud, or sprout". I don't see what that has to do with anything. Moe shows up a lot in anime to the point it's just annoying! Haruhi Suzumiya explains moe best in one episode of The Melancholy of Haruhi Suzumiya:
Examples of moe:
Meganekko-moe (Glasses Moe)
Miyuki from Lucky Star
Imouto-moe (Little Sister moe)
Mei Sunohara from Clannad.
You can just imagine her saying "Onii-chan~!", can't you?
Another word you should know is "moeblob". Urban dictionary defines moeblob as "A character who is moe to the point of lacking almost any other definable traits, physically or character-wise." Moeblobs should be avoided at all costs if you know what's good for you...