A hairdo is what a stylist gives you when he cuts and styles your hair. You might go to the salon to get a fancy hairdo before your cousin's wedding.
Hairdo is an informal word for "hairstyle." It's the way your hair is cut, dried, and arranged on your head, especially if there's some effort put into it. The way your hair looks when you roll out of bed in the morning isn't a hairdo, and pulling it back into a ponytail or covering it with a bandanna isn't a hairdo either. The elaborate beehive piled five inches high on your grandma's head? Now that's a hairdo.