Florence gets left for the same girl, twice
The novel ends with Dowell accepting Nancy into their dream house where he will take care of her and nurse her back to health, presumably winning her heart in the meantime. In other words, John ends up with Nancy. That's ironic because it means that the Florence's husband ends up with the girl that her boyfriend left her for. This Nancy girl is apparently impressive, since two men were competing for Florence and then stopped pursuing her entirely.
Florence's agony from Edward's love for Nancy
As mentioned, Edward cheats on his side girl (John's wife Florence) by pursuing his own niece. Florence kills herself from the pain of the disappointment, but it never really occurs to her that she has been betraying her real husband the exact same way for nine years. She has no shame for her unimaginable treason against her own marriage, but she fully indulges in her emotional victimhood, to the point of suicide.
The irony of affairs
Because of the nature of marriage, affairs should be rare, right? Not in this novel. There are nearly a dozen instances of cheating or affairs in the story, either in flashback or in the plot itself, which goes against the reader's assumptions about marriage, given the nature of marriage (it is an oath to God and man, so these four fairly traditional English folks are shockingly lax on the issue). Even the main character starts his daydreaming for Nancy while he is still married (although who could blame him? His wife never consummated their marriage).
The irony of superiority
This novel is highly concerned with superiority and inferiority. Just by the plot structure, it seems that this topic will be on full display (after all, of the two best friends, one hasn't even slept with his own wife, and one has slept with both wives). The superiority that Edward believes about himself proves to be ironic though, because like Florence, he kills himself at the first sign of true rejection. In other words, he pretends to be confident and powerful so he can impress women, but he doesn't have the emotional fortitude that John Dowell has, for instance.
The irony of Dowell buying the Branshaw Manor
Perhaps one of the reasons Dowell was rejected by his own wife was because she wanted to end up in a big fancy mansion, and Edward seemed more likely to provide that (that's what John believes about her anyway, and he should know having spent so much time with her). In that case, the ending of the story is ironic because Dowell does buy a big fancy mansion, the Branshaw Manor, and he moves in with Nancy to take care of her. So in other words, Florence stole from herself the life she always wanted, just by wrongly believing her husband was inferior.