Loyalty is the degree to which the inhabitants of a fief are content with their ruler. 9 is the highest loyalty, 0 is lowest. As loyalty moves to between 5 and 3 there is a greater chance of unrest, which reduces taxes raised. Loyalty under 3 causes rebellions, making it impossible to raise taxes, and forcing you have to pillage the fief to suppress the rebellion.  If a fief is raided or pillaged, its loyalty declines.  This is a favorite tactic to drive a fief into rebellion, thus denying the owner any income from it.