Possible causes of activation problems:
1. Your antivirus is blocking access to gs.apple.com.
2. Your phone is jailbroken.
3. Your computer has been used at some time in the past to jaibreak some iOS device (not necessarily the phone with the problem), and its network database was corrupted by the hacking software that was used.
4. Apple's activation servers are down (very rare, and never for more than an hour or so).
For 1. try disabling your antivirus.
For 2. & 3. you need to go somewhere other than an apple forum for help. Although you can try deleting lines containing gs.apple.com from your "hosts" file on your computer.