Derived from when someone is really drunk they try to "Irish whisper" something to someone and everyone hears it because you are too drunk to keep your voice down. Guessing it is called "Irish" because the Irish are known for love of drinking alcohol?
If you are speaking in a normal or loud tone "Hey Bill check out the hot girl next to me with the big tits! Isn't she hot?" You will in fact be doing an Irish Whisper.