Regenerate variant group ID is for Walmart functionality. All variant listings on Walmart require what they call a variant group ID, an identifying number that links all the variants together within Walmart's system. When a creating a variant listing from scratch in LM we provide one automatically.
However, when single listings are merged together into a variant listing the newly formed variants need a variant group ID. Clicking the Regenerate variant group ID button will assign an ID to the new variants. This only works while in the Walmart edit listing page of one of the variants. It can be found under the action icon.