I believe the other two answers are slightly off. In this case, the effects team is using a term more commonly applied to props and costumes: The "hero" (or "hero prop"/"hero sword"/"hero vehicle"/"hero costume" etc.) is the most visually detailed of a set of similar items fabricated for the film.
Think of Finn's stormtrooper helmet. At various times, the character will need to perform stunts, do long nights on location, and remove the helmet in closeup. The stunt man will need several cheap, well-padded, under-detailed helmets. The lead actor's helmet for normal full-body shooting will require comfort and durability, but more detail. For the climactic removing the helmet scene, he'll need a "hero" prop, with working lights, interior detailing, and some real heft to it.
In the Black Swan clips, notice that the plate (shot meant for compositing with other shots) referred to as the "hero" is always the one featuring the actress most prominently, with the most set visible, the least greenscreen, and the most careful lighting. Essentially, it's the "beauty" portion of the final shot, charged with establishing the reality of what we're seeing, so that the effects team can disrupt it.