From what you originally wrote it sounds like the phone is stuck with a screen like this:
As Jon points out in his answer, this isn't saying that your phone is connected to iTunes, it is saying that a serious and unrecoverable fault has developed with the phone's operating system and you need to use iTunes to attempt to fix it.
This message can be displayed for both software and hardware faults which affect the running of iOS.
Unfortunately with a phone in this state there is little to no chance of recovering your data if you didn't use iCloud to do backups, we need to reinstall/restore the iPhone's operating system.
There are different levels of restore, and I suggest given the situation with the device we jump straight to a DFU restore, DFU (Device Firmware Update) will restore the operating system and the boot loader.
Important: Do not proceed with a DFU restore if your iPhone has been jailbroken.
The first step to getting the phone to restore in DFU mode is to put it into that mode:
- Connect the phone to iTunes.
- Hold the home button and sleep/wake button together until the screen goes black.
- Release the sleep/wake button and keep holding the home button for 10 seconds.
- The phone should remain with a black screen, but iTunes should recognise the phone is connected.
- Follow the iTunes prompts to restore your phone.
- The device should restart.
If the phone fails to restore after performing a DFU restore then it is likely a hardware issue with the device and you'll need to seek support from an Apple Store, or Apple Authorised Service Provider, you can find out more here: https://checkcoverage.apple.com