Now, ignorance - in a general sense - is what constitutes our mental life: we can sense things (receive impressions) but never have complete knowledge - we cannot know HOW life works, how electrons and quarks can exist, or even if they do exist in the way we've imagined them.  Our ignorance is general, complementary to our little bits of knowledge. 

Beyond this, we also create from our sense impressions, new impressions - pro-facta you might call them:  a class of impressions not based on direct, immediate, concrete sensation, but rather things deduced or guessed at or constructed from intellectual conclusions we have made.  The realm, in other words, of ideas - such as the numeric world of algebra or the hoped-for world of an afterlife.  We can construct and impress these images on our selves. 

And then there is another category - God.  We fight over what God is because no one can truly prove it one way or another, as you might with a question of a rock's concrete qualities.  A bridge that stands against the wind is pretty good positive proof of an engineer's theories.  Given the ignorance, we shouldn't fight about what we don't know and can't demonstrate - but our urge to know (our innate dissatisfaction with our own ignorance) also engenders belief, in which we for emotional reaons enshrine pro-facta as hard facts or even as divine facts.  And if one gets onto the Platonic bandwagon of divinity, counting the divine as more real than reality, one gets into a war of Belief against Belief. Because every individual believes that he or she is right, and the rest of the world mistaken.

In a simple sense, the word 'belief' denotes the indefinite realm of the pro-facta.  I say, "I believe it's two in the afternoon," meaning it's my hunch that it is two, but I believe it and don't know it because I don't have my watch on. 

But 'belief' in a hard sense denotes something else.  It is the psychological realm of the True Believers, whose lives are dedicated to the pro-facta that they have enshrined as more real than real.  And it is here that the biggest fights start - not because of the necessary non-existence (in a technical sense) of these Beliefs (they are ideas, not things) but because the Beliefs are used to serve our own impulses, emotions and psychological needs.