Avoidance refers to a player's ability to completely nullify certain attacks. For melee, dodge, parry, and miss are all different ways to avoid the attack. For spells, resistance can raise your chance to completely avoid an attack. Bubbles from items and abilities, such as [Power Word: Shield], use absorption and if strong enough, can completely avoid an attack. There are bubbles that avoid both spell and melee damage or only one type.
Avoidance should not be confused with mitigation, which is the partial reduction of an attack. Block and armor for example can never give avoidance, but can give very significant mitigation.