For most iPhone users, the message asking you to connect your iPhone to iTunes may mean you have a software update. If you have recently dropped or otherwise damaged your phone, you may have a software glitch that requires an iTunes recovery. If your iPhone is jailbroken, you may also receive this message due to incompatible software. Apple does not support fixing the latter error.
If your iPhone needs a software update, launch iTunes on your computer and update your software on that end first. Your iPhone will work best if you have the latest version of iTunes on your computer. After any computer updates finish, plug your iPhone into a USB 2.0 port on your computer. Do not use an external USB hub or a USB port on another device, such as a keyboard. Follow any prompts on your computer screen to update your phone through iTunes. This will take several minutes, as iTunes will back up and sync all of your data first.
Follow the same procedure as you would for a software update if you suspect your phone is damaged. In this case, the message indicates your iPhone needs a connection to iTunes to repair its software. If the message is the result of a software glitch, iTunes may ask if you want to recover or restore your iPhone. Choose "Ok" and follow the prompts to recover your phone. Recovering will restore your phone to its original state, and then you can re-load your apps and other items from your latest iTunes backup. You will need to re-enter your email information and other linked account information on the phone once your restoration is complete.
ITunes may indicate that your phone is in recovery mode when it is not. If you get this message and you are sure your software isn't damaged, wait several minutes. It may go away and iTunes will complete a normal software update. If it does not, disconnect your iPhone and reboot your phone and your computer, then try again. If this does not work, you may need to do a full recovery on the software. ITunes may also experience update problems if you are not logged into your computer as an administrator, so always perform updates from the Administrator account if you have more than one user account set up. Unplugging all other USB devices can also help if you experience trouble with your iPhone connecting to iTunes.
Consult Apple's support staff, in person in a retail store or over the phone, if you continue to have trouble with the "Please connect to iTunes" message. If you receive the message on a jailbroken phone, your warranty is void and the Apple staff may not be able to help you, as Apple considers this unlicensed use of the device.