Respinning refers to the entire re-fabrication of a wafer. Although this is usually done following a hardware patch in the original design, it may also refer to situations where the original design needed to be modified or enhanced further. Respinning involves producing new masks which makes this process a very expensive option.
Respinning is the most effective way to fix hardware issues, however it's often the most expensive option and is therefore usually a last resort. Respinning incurs considerable engineering cost and possible time-to-market delays. Additionally, respinning must undergo rigorous validation in order to ensure no new problems are introduced in the process. It's for this reason that complex SoCs typically include some form of programmable hardware (e.g., microsequencer) in order to facilitate hardware patching in software.