It's possible that your screen or backlight has failed. If a restart doesn't fix the problem, you should have it checked out at the Genius Bar at an Apple Store or an authorized repair centre. If it is a hardware problem and your warranty hasn't expired, you'll either receive a replacement or have the screen replaced at no cost.
The restart is done by pressing and holding the home and power buttons simultaneously until the Apple logo appears, then releasing both buttons and waiting for the iPhone to restart.