We currently have some forging dies that the forging house is telling us that they need to "resink" them. Is anyone familiar with this process and could offer explanation?
Sinking a die refers to producing the cavity that does the work.
Therefore, 'resinking' suggests that the cavity edges are worn out, the resulting product is out of spec, and the die block can be salvaged by removing material.
If, e.g., the die block had cracked, you would not have the resinking option, but would have to buy a new die block and sink a new cavity.
Sinking refers to the Sinker EDM process, which is used to manufacture the impression in a block of tool steel for use as a forging die. The official/technical term is Electrode EDM (in contrast to Wire EDM). Google some combination of sinker (or electrode) + EDM + forging + die and you should gets lots of hits.