He's referring to an essay by Roland Barthes, which is basically about two things. First, there's no truly original writing, as the writer is usually rearranging a lot of older material, using existing tropes, motifs, etc.
The other thing, which I think basenji hinted at is that once the a work of literature is completed, it becomes independent of the author. In order for it to live, the author has to die, I think that's what he says, which can, again, be interpreted in two ways.
Firstly, writer is as reader of his own book as any other reader, so whatever interpretation he offers is just one of many.
The other thing is that author is usually the person who, sort-of, guarantees the meaning of a literary work, guarantees that there is some overarching theme or solution to the problem, so to say. If you "kill" author, you "kill" the need to go after that particular meaning, so plenty other meanings arise. You achieve some kind of democracy in reading, whether with always having an author in mind, it's a tyranny of one intended meaning.
I'm much more of an intuitive writer and not so much with the technical aspects, I just go with what feels right and do it that way.