If something is ironic it's unexpected, often in an amusing way. If you're the world chess champion, it would be pretty ironic if you lost a match to someone who just learned to play yesterday. Ironic is the adjective for the noun irony. In contemporary speech, when we call something ironic, we often mean sarcastic.
What makes something ironic?
In general, irony refers to a clash between expectations and outcomes. Typically, the outcome is the opposite of what someone wanted or hoped for. It's ironic, for example, when your boss calls you into her office, and you're expecting a promotion, but you instead find out you've been fired.
What is a good example of irony?
A fire station burns down. This is unexpected because one would assume the fire chief would keep his own building safe. A marriage counselor files for divorce. This is ironic because the expectation is that a professional who coaches couples through rough patches would herself have a strong marriage.