Bad connection, wiggle it a little bit see if that helps, or restart your computer then try plugging it back in. Does your computer have another slot to stick it in? Try using that one. If all this still doesn't help. Call the place you bought your phone and see if it's the phone connector.
If nothing happens when you plug your iPhone into the computer, the device has not been recognized by the computer. You can try restarting the computer and plug in the device again. If this does not happen, there could be a problem with the USB ports of the computer.