Essentially, Brazil is mired in corruption. The national oil company, Petrobras, has been funnelling billions of dollars to the Government party, the PT (Worker's Party), and its allies. The country is also in a massive recession (GDP fell by 3.7% last year and probably this one too), inflation is going worryingly high, and the budget deficit is higher than Rousseff's approval ratings, which is all sorts of amazing (10.7% deficit vs 9% approval). The Real has collapsed against the dollar, half of the Deputies' Chamber (the House) is under investigation, including its President (the Speaker), Eduardo Cunha, who personally authorised the Impeachment after Rousseff's party approved an investigation on Cunha... in short, any semblance of Government is gone, the country is unmanageable, and, unless there is a fresh new political cycle, Brazil is going to the doldrums.
The thing is: if Brazil were a Parliamentary system, they could have simply voted on a motion of no confidence on the Government and called for new elections. Over 60% of people want to get rid of her, and let us remember that she won her second term in a squeaker (3 million votes from over 100m+ cast). But, since it's a Presidential system, with fixed terms and no legislative oversee on the executive, they had to essentially make up some excuse to remove her from office: apparently she hid the budget deficit before the 2014 elections. She's most likely going to be removed and replaced by VP Michel Temer, from the centre Brazilian Democratic Movement Party (PMDB), who has the largest plurality in Congress (still way short of a majority, the Brazilian Congress is utterly out of control) and will try to somehow form a national unity coalition with everybody else in an attempt to save the country from economic catastrophe before actual elections can be called in 2018.
At this point though, they'd do very good to change the Constitution from start to end, since there are so many details of public spending and other day-to-day measures set in stone there that make writing a budget almost impossible; not to mention the utter ungovernability of the country. If they started splashing out petrodollars all over Congress is because there are so many different parties (20), most of them tiny, that the only way to put a majority together is throwing bribes left and right.