Different literary theorists operate under different assumptions concerning the role of readers in production of textual meaning.
Traditional historicist and philological criticism aims at discovering the ways in which an original audience might have read a text, and thinks that the most important response. Much of Biblical criticism, and the study of sacred texts, also focusses on historical readership.
Many postmodernist critics, including Derrida, Barthes, and Foucault, want to liberate the text from the tyranny of authorial intention, and are interested in how the site of meaning production lies in the reader and the reader's response and reading process.
Iser and Jauss, and others concerned with reception aesthetics, see meaning as produced between the intersection of the reader's and the writer's historical circumstances.
Stanley Fish argues that meaning is produced by communities of interpretation.
Textual meaning is created as the result of an act of communication between a sender and a receiver. We usually think of the sender as the creator of the message, but that’s really only half of it. No message is ever received with exactly the same meaning with which it is sent, because the sender and the receiver have different ways of processing information. Therefore the receiver, or the “reader” in your question, has half of the responsibility for the message.
We usually understand “textual” as a reference to something written (although it doesn’t have to be). Think about how different people perceive words differently. When we perceive the words of a message a certain way, it determines the message we get. If a word has an even slightly different shade of meaning to me as it does to you, a written message using that word will be different to me than it is to you.
Here’s an example. Early in the play The Tragedy of Julius Caesar, Cassius says to Brutus:
When Cassius uses the words “gentleness” and “love” here, referring to his friend Brutus, it elicits a definite reaction from high school students who are reading the play. Since this is no longer the way two male friends would talk to each other, some of today’s students perceive the relationship between Brutus and Cassius to be of a homosexual nature. Shakespeare’s intention is not to make his reader believe that Cassius and Brutus are homosexual, but today’s reader may assume they are. This is an pointed case, but the reader’s responsibility with regard to textual meaning here includes understanding the context in which the text was produced. Without this understanding on the part of the reader, the message is something different than what the sender intended.