Anvilicious is a portmanteau of the words anvil and either delicious or malicious. Exactly which one depends on the extent of the anviliciousness. The term is used to describe works of literature, film, television or other media which are so heavy-handed and unsubtle about delivering their point or moral that it's like being hit with an anvil. Exactly how offensive this is depends on the viewer and the particular point being hammered home: one viewer might feel that some anvils need to be dropped, while another might be quite annoyed by it.
The word was coined by those maniacs over at TVTropes.org, the online compendium of television (and film and other media) tropes and idioms.
It's an eminently useful word. Many things are anvilicious. A lot of the terrorism-related entertainment that came out in the wake of September 11, 2001 positively carpet-bombed anvils on unsuspecting viewers. Most so-called "Christian childrens' literature" is anvilicious in the extreme. (This isn't necessarily bad - some of the life lessons are valuable, even if you don't agree with Christian dogma - but the feeling of indoctrination is unequivocally present). Mark's Story is another classic example of anviliciousness.
The exact reason why so much of the heavy-handedness out there relates to either politics or religion, or to morals, not infrequently descended from religion, is pretty easy to see. After all, if you hear a message all day, every day for most of your life, it's going to have an effect on you whether you want it to or not.