in the sense that you anticipate one thing, and the opposite happens

To give a (rather funny) example of irony. When I was still living with my mom about 10 years ago, Something had happened where we had no gas (which means no heat or hot water). It was winter so taking a cold shower in a cold house was not a welcome idea. I worked at IBM at the time and there were showers in the locker rooms at work, so I brought a towel and would shower there. So, I go to take a shower there and the water was scalding hot (the cold water pipe in the shower stall was apparently blocked allowing only hot water to go through).

Sarcasm is an example of using irony in a biting, cynical way.