"Irony" is the use of words to express something completely different and usually opposite to the literal meaning of the individual words.
Example: Imagine a friend coming up to you on a cold and rainy day and saying: "Another perfect day to go to the beach!".
"Sarcasm" is the use of irony to hurt or offend people.
Example: Imagine one of your friends has just failed an important exam and you say to him: "Congratulations on your brilliant academic results!".
Hope that helps