So combat has changed? Yes, conflict is a new set of mechanics, but it goes much further too. No more will you accidentally kill the target you are fighting when you want to subdue him. Though weapons like swords naturally do lethal damage to the Vitality track, the swordsman now has a few new options to better control the situation.
Flat of the Blade can be used to inflict non-lethal damage to the target's Resolve track instead. A skilled swordsman also has the option to humiliate his opponent, rather than harm him, placing damage on his Reputation track instead. Usually this is described as cutting your initials into his clothing or what have you, but it could just as easily be done by causing him to trip, stumble, or otherwise show him up to be a lesser swordsman.
Pulling the Blow, is another useful option. Just because you rolled a critical, and your weapon damage + VP score is silly high, doesn't mean you have to start cutting people in half. Using a dueling weapon gives the character the opportunity to inflict precise wounds, up to your maximum damage level! This is very handy when fighting against an opponent with a dueling shield.
Because the setting is one that supports heroic combat, swashbuckling, and dueling, these abilities are available only when in melee combat. Standing at range and shooting with a blaster... well, let's put it this way: "This was your father's dueling blade, not as clumsy and random as a blaster, a more refined weapon for a more refined age."