Irony is shown when Emma considers her attraction to Mr. Churchill. She is such a match maker toward Harriet that it is ironic she can't tell when she herself is in love.
This irony is compounded with her indecision in how to respond to the news of Mr. Churchill's secret engagement to Miss Fairfax. She knows she ought to feel wounded by his insincerity, but knows she isn't wounded--and so feels ambivalent. Yet, another irony creeps in...how will society perceive this shift in affection?
Not knowing how to feel due to the concern of the way society interprets the situation is ironic in itself, but this was a concern of great import at the time.
So now that Emma is all grown up, she is ironically still in need of Mrs. Weston's guidance in the matter.
This is one example of the way Austen shifts from personal to intrapersonal and social irony.