わたし (watashi) is "I" in situations such as talking to a friend or teacher. Girls also tend to use it more than guys (guys have boku and ore etc) . わたくし (watakushi) is when you are speaking in very formal situations such as talking to a business manager or like your work boss etc. It is also very, very old and hardly ever used anymore as even in those situations its not ALWAYS used. I have heard it used in a few speeches recently from government officials though. Anyway, to put it simply its ridiculous formal way of saying "I".