For those living out of EU and who aren't interested in the topic (in very short):
Article 13 (Article 17 because politicians renamed it 3 days before voting)
Requires “information society service providers” – user-generated information and content platforms – to use “recognition technologies” to protect against copyright infringement.
Even small websites, or platforms based on open sharing, are required to comply with Article 13.
Moreover, automatic "recognition technologies" will most definitely also block content that is not copyright protected - therefore being censorship tool.
Article 11 (Article 15 due to same reason as above)
Gives large press organizations more control over how their content is shared and linked to online. This could mean that you would need a license to link to content (might even be any content).
Again, small companies and individuals are put at huge disadvantage compared to large corporations.
The actual extent of how much damage this will cause is unknown, as it may depend on how good the law implementation is done by specific member state. From my experience with administrative, if there is any way to abuse law to punish anyone - administrative in my country DOES ALWAYS SO.
It is also possible, any service available in EU (hosted elsewhere) might be required to comply (again, this has to be resolved within 2 years in each member state). This may end up in multiple services and sites simply being blocked for the EU (as we've seen with the GDPR nonsense).