The statement that describes the significance of the Mexican presidential election of 2000 is: it demonstrated that free elections could lead to a peaceful transfer of power.
The Mexican presidential election of 2000 was significant because it marked the end of 71 years of one-party rule by the Institutional Revolutionary Party (PRI) and the beginning of a multi-party democracy in Mexico. The election was won by Vicente Fox from the National Action Party (PAN), who defeated PRI candidate Francisco Labastida in a free and fair election.
The peaceful transfer of power from the PRI to the PAN demonstrated that free elections could be held in Mexico and that power could be transferred peacefully between political parties. This was a significant step forward for Mexican democracy and helped to strengthen the country's political institutions.
The other statements - "It brought on the beginning of communist rule," "It led to the rise of a military dictatorship," and "It showed that the rise of authoritarian rule could not be avoided" - are not accurate descriptions of the significance of the Mexican presidential election of 2000.