The Confessors were a group of women who ruled the Midlands and saw that laws were adheared to. They also removed leaders that were corrupt from power. The assassinations were when Darken Rahl ordered the deaths of all the Confessors. Darken Rahl sent quads after the Confessors. The quads would find the Confessor, hunt her down, and then (after doing brutal things to her) kill her. Every Confessor, including Kahlan's sister Dennee, was killed. The reasons behind the killing were that Rahl wanted to wipe out truth and justice from the Midlands and "extinguish" the light of truth.
The outcome of the killings was the deaths of all the Confessors save Kahlan. The only way for the line of Confessors to continue is for Mother Confessor Kahlan to have children.
The killings are often referred to in the books by Kahlan, Richard, Zedd, and others on their side. Kahlan occasionally speeks fondly and wistfully of her sister Dennee. The assassinations are also alluded to in prophecy; an example is in Wizard's First Rule: "the last Confessor" this and that. They are also referred to in Faith of the Fallen when Kahlan thinks about how the Confessor line is always vital and the only way for more Confessors to be born is for Kahlan and her husband Lord Richard Rahl to have children.