Irony exists when what happens or is said is out of keeping with what is expected. For instance, for a nun to win an award from an organization called Atheists International would be ironic because you wouldn't expect a connection between nuns and atheists. Another instance of irony would be for someone to stand in a monsoon with an umbrella and say, "It's a bit damp." This would be ironic because it would be out of keeping with what was actual or expected.
Verbal irony is a literary device (a tool used for a specific purpose by authors) that is a figure of speech. Figures of speech are not meant to be understood literally. They must be understood figuratively: Their real meanings are different from the words' actual meanings. In verbal irony, which may be spoken or written, the writer/speaker expresses an awareness (maybe more of an awareness than other people have) of the contrast between what is and what should be.
Bret Harte makes use of the literary device figure of speech called verbal irony in The Outcasts of Poker Flat. There are several very good instances at the beginning of the story in which Harte employs the literary device of verbal irony to illustrate that the virtuous secret committee isn't really so virtuous.
One example is the statement:
There was a Sabbath lull in the air, which, in a settlement unused to Sabbath influences, looked ominous.
Harte uses this verbal irony based on the Sabbath to humorously show that the town, whatever it thought of itself, wasn't really a town devoted to doing good.
Another example is the later statement:
It was experiencing a spasm of virtuous reaction, quite as lawless and ungovernable as any of the acts that had provoked it.
This verbal irony uses the idea of virtue to show lack of virtue. It means that the secret committee of Poker Flats may think that they are behaving virtuously but that their behavior is really the same as lawlessness.
There are some other very good examples of verbal irony in The Outcasts of Poker Flat for you to find. One has to do with getting rid of "improper persons" and a reference to a sycamore tree. Another one has to do with "sentiment" and "equity" and "fortune."
To read more about irony, see the Encyclopedia Britannica.