(pronounced moé or moe-eh as it is a Japanese word - meaning to Burn or Burning Feelings, from the verb ↗moeru) Titles that have a character or characters who are generally young in age, have a naive or innocent view of life, and "some obvious sympathetic weakness they work hard to correct" would be considered moé. A character or personallity trait that "elicits a protective or loving response from the audience" would also quallify (quotes taken from Wikipedia). Mahou Shoujo Lyrical Nanoha A's would be considered a moe title because of the wheelchair-bound character of Hyatte-chan. In modern terms moe has been evolving to the point where moe may apply to objects and not just young girls. Unfortunately moe can be taken to the extreme. See:Lolicon
This is a term coined to identify things like jiggling breasts, cleavage shots, panty shots, bra shots, closeup shots of women's breast, legs, butt, etc., and mild nudity all for the purposes of "servicing" the audience and having no relevance to the plot or characters of a series. The term has a second meaning covering things like massive action sequences, explosions, fights, etc., but it mostly refers to the first meaning.