Something outrageous is extreme, over the top, beyond reason. It's hard to believe, and usually not in a good way. If the police came in and stole your TV, that would be outrageous.
If you know what outrage means, then you're on your way to understanding outrageous. Outrageous things make people outraged, really angry, or astounded because they're just so ridiculous. If your teacher gave everyone an F for no reason, that would be outrageous. If a friend spilled your secrets to everyone: outrageous. Lady Gaga rolling up to the Grammy’s in a giant egg? Totally outrageous, but in a wacky and extravagant kind of way.