The irony of human experience
One might say life itself is ironic, and therefore, says Barthes, realistic art will obey the same rules of irony that human experience does. By starting in medias res, a novel reminds the reader of a day in their life, which always starts somewhere in the middle. By invoking religious themes in an artwork, the reader is forced to consider the unanswerable questions of life. Life is ironic because nothing is explained us about it except in what others have written.
The irony of language
Language itself is simply riddled with irony; that humans evolved to speak is ironic in some ways. The diversity and accidental beauty of language is ironic when considered alongside life's inherent meaninglessness. Therefore, good prose about life's meaninglessness is ironic, because the language used to describe meaninglessness is meaningful, especially to the kind of reader who reads a good sentence and says, "Wow! How beautiful."
The irony of symbolism
Artists often make this mistake: they attempt to use symbolism to instruct the reader about morality or something similar. But that misses the mark because symbolism is ironic. The magic of a symbol is that it invites the reader to attach their own meanings to the text. Symbols are as simple as building a bridge of association between the character, the author, and the reader, but the real magic is in the symbolic subjectivity, because the signs will mean different things to different people.
The irony of experience
Experience is ironic, especially when considered in tandem with innocence. Innocence leads young humans to draw conclusions about reality and life that adult life removes wholesale. If childhood is about individual growth and play, then experience is something like horror. Life is much more chaotic and frustrating and difficult than innocence suggests, and Barthes' view of literature is that it is a way of showing experience to people so they won't be blindsided.
The irony of meaning itself
That things "mean" things is ironic. It does not explain itself. Why should a rose be more than a flower? But it also a religious symbol, and it is a sign of romance and sexuality, and roses are also very beautiful, which is a kind of meaning perhaps. So if a simple flower can have meaning in it, why should human life be so meaningless? Barthes feels art exists to answer this exact question.