This was a milestone, but it's not quite a done deal yet. Now that it has been approved by the European Parliament, it goes to the Council of Europe in April. Assuming it is approved, then EU member states each have two years to implement the directive into their own laws. Since the language of the directives is not very specific, different countries will interpret the directive in their own ways, a further complication for service providers.
The devil is in the details of the implementation. I don't personally believe that the sky is falling just yet, as the video @Dracula posted claims. One of the vested interests that wasn't mentioned in that video was the tech sector, which has its own agenda here and has been doing its best to scare the crap out of everybody by assuming the worst possible interpretations of articles 11 and 13. The reality could easily be far less radical.
When the EU passed its General Data Protection Regulation, a huge fuss was made about how it would be an intolerable burden on service providers. Yet somehow, most companies have managed to adapt and life goes on. John Gilmore, one of the founders of the Electronic Frontier Foundation, famously said "The Net interprets censorship as damage and routes around it." I think the same might turn out to be true of this directive. I'm not happy with it, but I'm pretty sure that reports of the Internet's death are premature.