One could argue that the biggest irony in Pride and Prejudice is that two people who seemed so completely incompatible—Elizabeth Bennet and Mr. Darcy—end up falling in love and getting married.
For much of the story this seemed like an unlikely outcome, to say the least. The brooding, aloof figure of Mr. Darcy always seemed far too proud to marry beneath himself. He was pretty scathing about the Bennets, seeing them as frightfully vulgar and ill-bred, certainly not the kind of family he'd want to marry into. And yet, miraculously, he's able to put aside his overweening pride and realize that Lizzie is the woman for him, whatever his sniffy relatives may think.
As for Elizabeth she has somehow been able to overcome her prejudice in marrying Darcy. She always saw him as such a proud, disdainful individual. Though rich and handsome, his snobbishness was always a major turn-off for her. And when the scheming Mr. Wickham starts telling tales about Darcy, Lizzie is only too ready to believe his lies.
Yet she too is able, by a remarkable series of events, to overcome her preconceptions. On the face of it, this is no less ironic than Mr. Darcy's own quite remarkable transformation.