What does 'moe' mean? I've now watched quite a few anime and I'm still at a loss as to what the term moe represents. Is there an agreed upon definition for it? If a character is moe, what does that mean?
Here is an academic paper1 with an analysis of the concept of moe, including its history and origin, relationship to the socio-economics of Japan, previous academic studies of moe, otaku and fujoshi psychology, and a very in-depth analysis of what moe actually is. 

A short table of contents of the topics covered:


Japanese critical discourse
Emergence of the moe form
Otaku discussions of moe
Moe desire and sexuality
Moe in relation to 'reality'
The female approach to moe
Fujoshi exposing virtual potential in reality


To quote from its conclusion,


  Both otaku and fujoshi describe moe fantasy as 'pure,' or set apart from reality, and it precisely because it is pure that it can give birth to such perverse and polymorphous possibilities. The moe character is a 'body without organs' and it engenders virtual possibilities without limits or control. Stated another way, moe describes affect, or an unstructured intensity in response to the virtual possibilities of fantasy characters. Whether it is the girl-child popular among men or the homosexual boys popular among women, these young characters are not part of the 'real' world and do not demand their partners be socially mature and responsible adults; with moe characters, men can experience love outside the confines of manhood (defined by work) and women love outside the confines of womanhood (defined by childbirth).




1 "Moe: Exploring Virtual Potential in Post-Millennial Japan", by Patrick W. Galbraith. Published in the Electronic Journal of Contemporary Japanese Studies, article 5 of 2009; first published on 31 October 2009.