Irony in speaking is a matter of saying one thing and meaning something else. Irony in this sense can be either deliberate and intentional (Socrates) or unintentional (the speaker does not know that he or she is being ironic).
The term "tragic irony" refers to unintentional irony on the part of a character in a tragedy. Sophocles' Oedipus the King contains perhaps more tragic irony than any other Greek tragedy. For example, in the First Episode, after Oedipus refers to his personal motives, as distinguished from his "official" ones, for tracking down the killer of Laius, he says: "Such ties swear me to his (Laius') side as if he were my father" (Roche, p. 223). Of course Laius is in fact his father, as the audience knows. What is "as if" to Oedipus is reality to the audience.
Oedipus the King contains so many examples of tragic irony for the obvious reason that the protagonist does not know his true identity until late in the play and therefore does not know that he himself is the one whom he is looking for. His authority and security are illusory and soon to crumble. A split opens up, in the audience's perspective, between reality, on the one hand, and Oedipus' statements and actions, on the other. This protracted illusion is a larger irony that can be called "dramatic irony." (For a somewhat wandering definition of "dramatic irony" see the article "Irony" in Alexander Preminger, ed., Princeton Encyclopedia of Poetry and Poetics, rev. ed. [Princeton: Princeton University Press, 1974]. The nub of the definition is: "the spectators know more than the protagonist.")
The phenomenon of unintentional irony,
as in "as if he were my father," is in Greek tragedy the product of a situation
of which the protagonist is both unaware and also innocent, in the sense
that he or she is not (at least not entirely) responsible for it.
Tragic irony therefore leads back to dramatic irony, which leads back to
the causes, usually complex, that create the situations of tragedy.