Q: What are masterwork rolls?
A: Most legendary weapons are capable of being Masterworked. The masterwork system is a way for you to upgrade your favorite weapons to their maximum potential.
Q: What does it take to upgrade a weapon to a masterwork?
A: Upgrading your weapons, in broad terms, takes a small amount of glimmer, legendary shards, and, most importantly, Enhancement Cores.
Depending on what Tier your weapon is at, the requirements to raise it to the next tier increase the closer the weapon is to being fully masterworked (Tier 10).
Q: What benefits do I get for masterworking a weapon?
A: Each tier that you increase your weapon will grant a small buff to a single stat, chosen randomly when the item drops.
Beyond that, at Tier 5 you gain access to a kill tracker. At Tier 10, your multi-kills will generate orbs of light.
Q: So what are these "masterwork roll" stats?
A: These are the possible stats that upgrading your weapon will grant a bonus to. Depending on what tier you are at, you can grant anywhere from 1-10 additional points in any of the stats listed to your weapon.
Q: Any catch with this?
A: The Bungie API currently says that all weapons can potentially roll with all stats as their masterwork stat. This obviously isn't accurate, as Blast Radius isn't applicable to, say, Auto Rifles.
The list you see on this page is trimmed to only show stats that actually appear on the weapon. However, it is possible that Bungie has additional logic behind the scenes that further filters these
possibilities to, for example, prevent certain items from being able to have an Impact masterwork. Until Bungie modifies the API files to 100% accurately display which masterwork stats are possible on
each item, take what you see here with a pinch of salt.
Unfortunately the RoN heavies are a grenade launcher and an LFR, which are both hard to justify compared to rockets and machine guns right now for both boss damage and wave clear, but in a world where one of those weapon archetypes becomes good, you're looking at a free 10% damage buff versus Tormentors (including Nezarec) and Lucent Hive, which is a pretty big deal by origin trait standards. But alas, Koraxis' Distress has basically zero applications compared to a machine gun and Briar's Contempt needs Surrounded to keep up with the current meta DPS options, which is a tall ask.
The other situation is that, in the event you happen to like the Epochal Integration hand cannon, it also gets this origin trait, which means you can run a PVP loadout with that, Conditional Finality (a top-shelf shotgun that uniquely shuts down certain powerful options), and either heavy weapon (heavy GLs and aggressive-frame linears being actually pretty good PVP heavy choices) to get some free handling and reload on your hand cannon (the damage versus supers may also come up, but probably isn't the point here). This makes it reasonably competitive versus a comparably-rolled Rose, which seems to be the best legendary hand cannon right now. Rose still has huge advantages in range, AA, the lightweight bonus, and not requiring as specific a loadout unless you're going Elemental Capacitor though, and if you ground out a lot of Rose rolls when it was available, you likely have a better one even factoring in this origin trait.
In conclusion: good origin trait, screwed by RoN's weak heavy weapons in PVE, screwed by Epochal Integration being only okay in PVP. (Seriously, if they had put this on a half-decent machine gun...)