iOS 7 update requires approximately 3GB's of storage space. Tap Settings > General > About > Available
If there's less than 3.50Gb's of available storage, then you need to free up space.
If it's not a storage space issue, reset the device:
Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.
If that doesn't help, tap Settings > General > Reset > Reset All Settings