This usually happens when one loses the Internet connection while downloading the app.
The usual fix for this is to restart your device.
To do this:
1. Press and hold the sleep/wake button at the top right of the device and the home button in the bottom center of the face at the same time.
2. Hold them both until you see the screen go black. In some cases, you may need to keep holding them even after the red power off slider appears. If it does, just keep holding it.
3. Wait until the white Apple logo appears.
4. When this happens, you can let go - the iPhone is rebooting.
After that, the app should no longer be listed as installed in iTunes and you'll be able to download it again (don't worry, you won't be charged twice).