It means to make it hard to see or understand the difference between two things.

zamagliti razliku, pomutiti/srušiti liniju

 

The story said it was based on real events, but many parts were clearly made up. It blurred the line between fact and fiction.

The article blurred the line between news and opinion, so it was hard to know what was fact.

He joked with his kids like a friend, but when it was time to set rules, they didn’t listen. Blurring the line between parent and friend made things harder.