The Apt-X refers to a built in codec that takes the available Bluetooth audio and enhances it so you have a superior sound. In order for the Apt-X codec to be utilized both the headphones and the device that they are connected to need to have the Apt-X codec built in.
If the codec is not available in the device you are connected to the headphones will still work however you will not have the benefit of the Apt-X codec. If a device does not have the Apt-X codec built in you can purchase a device called a Bluetooth dongle with the Apt-X codec that will connect to your device and allow you to utilize the codec.
NOTE: Apt-X will not affect Bluetooth connectivity with a device.
For more information about APT-X, click here.