PICKIT 3 and 16F684 in-circuit debugger
MPLAB will tell you if the 16F684 needs a separate debug header - select the device using Configure > Select Device. You should see that you need an AC162055 header. The product web page also mentions it. It comes with an RJ11 connector, so you will need an adapter to use it with a PICkit.

The only debugging you will be able to do without the header is by using the simulator, or by inserting debug statements into your code and using a serial connection to your PC.