Plaza de Mayo has been the main political square for Buenos Aires since its May 1810 revolution. Today it's home of the Casa Rosado (Pink House) which is where President Cristina works. It is also close to a bunch of really important (and pretty) federal buildings. See below.
The craziest thing to me about this plaza is its significance in "the dirty war," which occurred during the military dictatorship through the 50's, 60's, 70's. During that time, the government illegally obtained, tortured, and killed anyone who opposed the regime, or who seemed to be sympathetic to the left.
The Mothers of the Plaza de Mayo began marching to draw attention to the children they lost (los desaparecidos) and were a critical part of bringing justice to some of those responsible. Today, some of the women who were killed for speaking against the government are buried here.
it's hard to believe that only 30 years ago, this somewhat liberal city was run by a military dictatorship that kidnapped, tortured and killed possibly up to 30,000 of its own people, but you can definitely see how the memory of this influences the people of Argentina today, which I'll say more about later.