Typically a newcomer (aka newfag) to 4chan's /b/ board who does not appreciate or partake in the more extreme activities such as posting or viewing gore, child pornography, or nonconventional pornagraphy. Usually a moralfag opposes animal torture or pics regarding it and will do what they can to voice their opinion on it. More recently, the term has been associated with the wave of newfags to /b/ who have supported the Project Chanology movement against Scientology. Most believe in using the "power" of /b/ for good or morality.
A typical moralfag response to animal torture "Dude, there's nothing funny or cool about killing a defenseless cat. I mean, its perfectly fine to look at dead bodies of humans and stuff but not animals. Let's start a IRL campaign against animal torture cause be is totally Fight Club!"