Frequency Range
The range tells you what frequencies it will measure. Audio frequencies run from 20 HZ to 20,000 HZ. Microwave frequencies run up to 30 or more GHz. Some counters have models or plug-in units for various frequency bands. Expect the price to increase with higher frequencies and wider ranges.
Power Range
The power range tells how strong a signal the counter will read. Also, some signals ride on DC voltage that the counter must withstand. If you want to read the frequency at the output to a transmitter amplifier, you need a counter that can withstand high power. But that's not necessary at the input to the amplifier.
Accuracy
Accuracy tells how closely the counter measures the actual signal. Specifications can be illustrated in percentages or parts per million. Although price usually increases with accuracy, technological advances tend to keep lowering the price of units offering adequate accuracy.
Resolution
The resolution specification tells how pure the signal must be for the counter to read it. Complex formulas describe resolution specifications and circuits, but your application really determines what resolution you need. Usually it isn't too great of a concern for most frequency-measurement applications.
Environmental
Environmental specifications tell what climates in which you can operate and store the counter, and include temperature, humidity and altitude. Some counters also include specifications for dust, pollutants, physical shock or vibrations.