What Is the Significance of “Longest Chain Rule” in a 51 Percent Attack?

The "longest chain rule," a fundamental consensus mechanism in PoW, dictates that the blockchain with the most cumulative proof-of-work (i.e. the longest chain) is the valid one. An attacker with 51 percent control can mine blocks faster than the rest of the network combined.

They secretly build a private chain, and when it surpasses the length of the public chain, they release it. The network then automatically switches to the attacker's chain, accepting its history, which includes the attacker's fraudulent transactions.