A good thread explaining the next steps: https://twitter.com/why0hy/status/1110514962366189568

TL;DR summary: The directive will have to be implemented in national legislations, a ~2 year long process. There are a bunch of contradictory laws and regulations to be reconciled. Your app or platform can probably ignore the new rules as they're too unclear and unenforceable - but do join trade associations that can provide good, reliable legal support.

[Edit] here's another article from EFF explaining the next steps:

https://www.eff.org/deeplinks/2019/03/eus-parliament-signs-d...