In general, the militaries of various Latin American countries affected politics by controlling the government at times in the countries' histories.
In many Latin American countries, the army was the most organized and cohesive force in the country. These countries had weak commitments to democracy (at best) and civilian governments often descended into chaos. When this would happen, the military would often step in and overthrow the government in an attempt to create stability. The military might then install a dictator like Juan Peron in Argentina or it might create a military junta to rule by committee.
The military interventions were not always motivated by a need for stability. At times, the military would simply intervene because military commanders did not like the direction that policies were taking in the country. An example of this is the overthrow of the Allende government in Chile by Augusto Pinochet.
Throughout the 20th century, many Latin American countries were ruled by their militaries at some point. In this way, the military had a huge impact on politics in the region.