It's a specific doctrine based on the diviniation of the cleric class, that says that Federal Elections are left to the state legislatures to run / facilitate. So far, America has been running their elections with the idea that electoral decisions are "ordinary" political processes, and decisions by the legislative branch in a state can be kept in check by either courts or governors, or whomever they appoint. This means that blatant partisan fuckery is supposed to be harder to get away with, as there are multiple points of failure. Under the independent state legislature doctrine (goat entrail reading), electoral processes are in fact only for the legislative branch of every state to decide.

This would be a bad thing for a multitude of reasons, but the primary one is that Republicans currently have a majority in pretty much all swing state legislatures, hence why they are pursuing this avenue of attack. The theory would allow them to bypass governors, election officials they didn't personally appoint, courts or even state constitutions.

This could be wrong, but I sourced it from here: https://www.brennancenter.org/our-work/research-reports/independent-state-legislature-theory-explained