The protests started in São Paulo because of the raise in the bus fares ("measly" R$ 0,20). This in itself is not a big issue, but the people were already fed up of mismanagement in the government. They claim there's no money for public transport but there's money for private transport (tollways, 0 taxes for cars), shiny stadiums for FIFA, astronomical salaries for the legislative...
The protests gathered enough people, and faced fierce, disproportional violence by the police. It became clear that, with the Brazil in the spotlight (Confederation Cup starting this week), the government didn't wanted people on the street. The situation escalated, and more people started protesting the following days in all major cities.
Now they are not protesting for anything in particular anymore, the protests are to show the insatisfaction of the population and how any protest gets suppressed with violence by the police. The São Paulo governor even applauded the work of the police.