King Edward IV is the older bro of Richard, Duke of Gloucester (a.k.a. Richard III) and George, Duke of Clarence (a.k.a. Clarence). When the play opens, King Edward IV is ruling over England, but the guy's health is failing. Everyone is sort of hanging around waiting to see what happens after he dies.
We don't see much of this character, but before King Edward dies, Richard dupes him into believing that his brother Clarence was plotting against him. (In fact, it was Richard.) Edward's death reminds us that family members can't always be counted on to be loyal or loving.
Psst. Compare Edward IV to another Shakespearean king who is betrayed by his brother – King Hamlet.