In the beginning of the Item Qualities section of Chapter 5 of the core books it notes that unless stated in the description of a specific quality, a successful attack must be made to activate a weapon quality, but it does not require that damage be done. Despite the high damage capacity of a lightsaber, there are still situations where it may not get through soak, armor, or other considerations.
As weapon qualities are typically the result of their attacks, a successful hit is required. Some, like Guided, can only be activated on a miss and are related to the specific nature of the weapon's attack. Simpler situations like Sunder, Knockdown, or Linked are directly related to succeeding in having the attack connect with the target.
It may cause some confusion when reading that some Qualities state on a hit and some don't, but as this inclusion or its absence does not contradict the text at the start of this section (on a successful hit...) the group can still follow the instructions and description as written. When things are different they are spelled out in the description of the Quality. This might appear as "...on a missed attack..." or something similar.
Description of Sunder
Sunder, on a successful attack, will damage a weapon or item by 1 step per 1 Advantage spent. Multiple activations are possible if enough Advantages are rolled, each damaging the item one step.
Sunder could be activated through the use of its listed cost of 1 Advantage, or the use of 1 Triumph.
Reasons for Using Sunder
The reasons for using Sunder during the resolution of a successful attack are many, connected to the specific scene, and to the players' points of view and culture of play. Some reasons might be to reduce armor or other defenses to enable more successful attacks later, to destroy a dangerous weapon to allow a different approach to dealing with its wielder, to reduce the threat from an opponent, to encourage a surrender, and other motivations tied to roleplay.
It should be noted that this is not an either Damage or Sunder choice. If you note the sequence of attacks, damage is resolved in Step 3 and Qualities in Step 4. Unless otherwise noted in the resolution of an Item or Weapon Quality (such as Stun) in Step 4, damage will be applied and in many cases lead to the narrative effects of the Quality.
In other words, on a successful hit, but regardless of whether damage is inflicted past soak, the attacker may add the effect of Sunder to the narration for the cost of 1 Advantage, and thereby choose to apply Item Damage to something openly used by the target. Four such applications in a single turn will destroy that item in a single hit. This includes things like armor.
Activating Sunder and/or Criticals
If trying to understand the benefit between choosing a Critical or choosing Sunder, the limitation of inflicting damage becomes relevant. To inflict a Critical requires that damage must get past Soak. Sunder only requires a successful hit. As some lightsabers can inflict a Critical for a single Advantage, this is can become a consideration in play.
Also, the needs of the scene may urge the character to seek avoid grievously wounding the target.