There are different "types" of irony, but to keep it simple I would say that irony is an event where something appears to be one thing on the surface, but in actual fact is very different or even the opposite of what it appears to be.
Here are a few examples:
When someone says "That's as clear as mud".
When you first hear it, you could easily assume the speaker is going to comment on how clear something is. But in actual fact, the phrase means the complete opposite of what was expected.
When an ambulance rushes to the scene of an injury, and runs over the injured person.
The idea of the ambulance rushing to the scene should normally mean that help is on the way. But in actual fact, the ambulance's presence causes further injury.
A traffic cop loses his license for unpaid parking fines.
Someone who you would at first impression expect to have an immaculate driving record due to his job, actually displays that the complete opposite is true.