What process takes place in this powerhouse of the animal cell? don't confuse this with breathing.

What happens in the mitochondria is a chain of many coupled red-ox reaction. In the respiratory chain, so called reduction aequivallents (NADH, FADH2) get oxidized by giving the energetic electrons obtained from sugars/fats during the glycolysis and the citric acid cycle to different carriers(they get reduced). This leads to the establishing of a proton gradient in the intermembrane space of the mitochondria.
A really important redox reaction is the reduction of O2 to H2O, where ADT and phosphate are joined to generate ATP. 
Sorry if the description isn't exactly chemically correct, it is certainly biologically right :)