The effect of Execute is clearly explained in the tooltip. If you don't like the feature, don't use it. If you don't know what a feature does and you don't like experimenting, then don't click the button. This new feature is intended to offer convenience and time savings to players who want it. Nothing requires that you use it.
It automatically kills the bosses you've already beaten in the section of your choice for 5 stamina each (same Stam cost as if you killed each one yourself). It doesn't effect bosses you haven't killed yet.