Aggravate means to make something worse, and irritate is to annoy. But if you use aggravate to mean "annoy," no one will notice. That battle has been lost in all but the most formal writing.

To aggravate is to make something go from bad to worse. Yet aggravate was first listed as meaning, "exasperate, annoy" in A Dictionarie of the French and English Tongues by Randal Cotgrave in 1611. But it's not exactly the same as irritate, darn it, and the sentences below get it right. In the news, aggravated often goes with battery, which is worse than simple battery (beating someone up), and carries a tougher punishment:

Knight was arrested for aggravated battery and resisting a police officer. (Chicago Tribune)

Tapia, 27, was charged after the confrontation with several counts of aggravated battery on a police officer and resisting arrest. (Reuters)

Regardless of pH levels, high-fat meats, dairy products, caffeine, chocolate, carbonated beverages, fried foods, alcohol and mints are known to aggravate reflux symptoms. (New York Times)

Irritate means to annoy someone. If you try to use irritate in the sentences above, it doesn't work as well. Irritate also means to inflame a part of the body, and in that sense, aggravate won't do:

Bedbugs don't spread disease, but they can irritate skin. (WebMD)

Gold chains are also very irritating to the neck and arms of an infant. (Eliza Leslie)

Despite four hundred years of English speakers using aggravate to mean annoy or irritate, there is a shade of difference. If you make something worse, you aggravate the situation. A bedbug will irritate your skin. If you're determined to annoy, use either.