This protest got a lot of people with different opinions together. As ridiculous as it sounds, some of them even want the military back in power. Some people had swastikas drawn on their flags. Some others just want someone else on power.
All they have in common is their hate for the current president's party, who won the last election with roughly 52% of votes.
The current party has been in the power for too long (Lula 2x 4 years, Dilma currently on her 2nd 4-year period). Petrobras, the largest company in the country is government-owned and run and lost 80% of it's value in the past 5 years due to corruption. The Brazilian Real devaluated 60% in 2 years. People have all the right to be pissed off. The biggest problem here is that the opposition is also very corrupt, so people are not protesting in favor of someone, but just against Roussef. Though situation.