Can anyone help me to understand this titration?

The theory for titration is that we should know how much chemical completely reacts with a compound of a fixed quantity. Potium permanganate reacts with hydrogen peroxide only in the acidified state, sulphuric acid helps increase the reactivity of the permanganate solution. As for your second question, it is straightforward. You add it slowly so that you can figure out the reaction between kmno4 and h2o2 based on how much kmno4 reacts with h2ho2