Characteristic of all of Jane Austen's work, Mr. Collins' proposal to Elizabeth is full of witty irony. The first instance of irony is that Mr. Collins mistakes Elizabeth's unwillingness to be left alone with Mr. Collins and her attempts to hide her embarrassment and humor at the situation through distracting herself with work as "modesty."
The second instance of irony is that his real reason for wanting to marry is that Lady Catherine de Bourgh advised him to. He states his first and second reasons for wanting to marry as that it is his duty as a clergyman and that it will increase his happiness, but the third reason concerning Lady Catherine he states that he should have mentioned earlier, insinuating that, really, it is his first reason.
A third instance of irony is that he assumes that Lady Catherine will accept Elizabeth's "wit and vivacity," and moreover that Elizabeth will "temper" both these things with "the silence and respect" due to Lady Catherine's rank. This is a huge ironic assumption for Mr. Collins to make because of course we have never seen Elizabeth hold her tongue or "temper" her "wit and vivacity."
A final instance of irony is that Mr. Collins is quick to assume that Elizabeth's refusal is a way of her being modest and that all modest young ladies refuse at first the men they intend to accept. Mr. Collins ironically interprets Elizabeth's refusal speech as encouragement and says he hopes for a more positive answer when he asks her again.