Okay kiddo, so you know when you write something for someone and they give you money to do it? Well, some journalists also do that. But this is not a good thing because it means they are not being honest about what they are writing.
Brown envelope journalism is when a journalist gets paid secretly to write something a certain way. They might write good things about someone, even if they are not true, just because they got paid. This is bad because it means people might believe something that is not true, and it can be unfair to others who didn't pay to be written about nicely.
Journalists have an important job to tell the truth about what is happening in the world. Brown envelope journalism makes it hard to trust what they say, and that is not good for anyone.