After restoring a backup in iTunes, the iPhone (or iPad/iPod Touch) will reboot, and then start up in the Welcome/Setup app. The setup app will review some of your settings, and have you help finish setting up. Depending on the settings files that were restored in the backup, you will see some or all of the setup screens (wifi setup, iTunes account login, iCloud approval, lock screen codes, etc.)
Depending on one particular file in the backup the setup program will prompt you to "Setup as New" or "Restore from Backup" -- if you see this after the restore, select "Setup as New" since we just restored a backup ;). It sounds like it's going to wipe the iPhone, but it basically means "do nothing and carry on."