An Apple iPhone blacking out could be a simple matter to resolve or a potentially costly one. If holding down the home button and the Sleep/Wake button on top simultaneously for 10 seconds doesn't produce the Apple startup screen, then your device could be out of power or seriously damaged.
The simplest explanation for an Apple iPhone blacking out is that you've run the battery down past a critical level. If the battery dies, your device won't present a flashy screen and clearly power down if the battery dies. Instead, the screen simply goes black and won't turn on. Plug the cord that came with the iPhone into your computer or a USB-to-AC adapter and wait a few minutes to see if the screen starts responding again.
If the iPhone's screen is still unresponsive after 20 minutes of charging, then the screen itself could be broken. Wires may have come loose inside your device or water damage could have fried its circuitry. You'll have to take it to an Apple Store or iPhone repair specialist to see what's wrong.