The bill had been in the works for years before the Snowden revelations, but they (especially the parts about the NSA spying on Rousseff) really kicked things into high gear. Rousseff asked for the bill to be treated with "constitutional urgency."
Marco Civil will provide for net neutrality (something we in the United States don't have), limits gathering data from internet users, and says that internet services used by Brazilians are subject to Brazil's laws -- even if those services (say, Twitter or Google) aren't provided by Brazilian companies. In turn, service providers will not be held responsible for content posted by their users.
Though the bill is being hailed as a step towards an open and free internet for everyone, it does have its detractors. Mozilla pointed out that there is a mandatory data retention provision that requires sites to keep user data for six months to a year. It also gives the government more control over the internet by forcing companies to follow Brazilian law. As we saw with Turkey and Twitter, that can be used against as well as for free speech. With the World Cup coming soon, Brazil could be keen to suppress the social media-fueled mass protests it experienced last summer. Then again, Rousseff "praised the protests as democratic," as Reuters put it, so she may well be just as proud of protests in the future. Like, for example, the ones happening in Rio de Janeiro right now.