The relationship depends on what type of operation you are doing with the counter. If you are doing event counting, then the counter source is the signal that you are trying to measure. If you want to measure the period of a signal, then the counter source can be one of the internal timebases (100kHz or 20MHz for the DAQ-STC on the 6024E), and your signal is connected to the gate.
For period measurements you can set the internal timebase with the Counter Set Attribute command. Take a look at the examples that install with NI-DAQ for details on various types of counter operations. These examples also describe how to connect you signals.
Regards,
Brent R.
Applications Engineer
National Instruments