Among other post-structuralists and deconstructionists from the 1960s to the present, Roland Barthes shows that the meaning of a text is not owned or fixed by the author's intent. Barthes is not describing the literal, physical death of an author. He is being figurative in that, free from any attribution to an author, a text opens itself to more interpretations by the reader. 

The meaning of a text is not set in stone and it is therefore not beholden to any pre-established structure, perspective or any interpretation. In "From Work to Text," Barthes explains two philosophies of writing. Thinking that writing is a "work" suggests that this writing is set in stone, like a monument. Therefore, the meaning of a "work" is fixed to an author or a predetermined structure of thinking. Barthes chooses to think of writing instead as a "text" in which he considers writing to be open to interpretation. In a sense, Barthes sees texts as orphaned from, and therefore free from, the (author)ity of the author. 

To give a text an Author is to impose a limit on that text, to furnish it with a final signified, to close the writing. 

Barthes understands textuality to be a moveable, woven tapestry and intertextuality weaves the tapestries of individual texts together. A writer or a reader does not have authority over a meaning of a text. A writer or reader approaches a text and, writing or reading, essentially holds some strands together in a construction (interpretation or perspective) and that is where/when the meaning emerges. So, the meaning of the text is produced via this interaction between reader and textuality. This is a much more fluid concept of writing in that meaning shifts with the differing perspectives of each reader who, being subjective, will hold different strands of the tapestry together and, being free from the authority of any author, the reader will construct different meanings: 

. . . the reader is without history, biography, psychology; he is simply that someonewho holds together in a single field all the traces by which the written text is constituted. 

The "death of the author" simply means that the reader takes charge of producing meaning. Text does not belong to anyone. Text is simply there waiting for someone to make a meaning. This idea acknowledges the fluid function of textuality and it is also a rebellious doctrine because it is inherently a challenge to (author)ity.