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Your question is so incredibly general I'm not sure exactly what you are really asking, but in synchronous logic, the counter will change its value on a clock edge. Which edge it changes on, and whether or not it changes its value on every edge, and what the next value will be are all determined by the RTL that you write.
So without the clock, you have no counting, thus the clock is very significant for a counter.
First of all, Your question is not clear. "significane of clock, how it is related to counter".
Clock is a very important signal in Digital electronics. In synchronous designs, every process is based on clocks. Suppose a Processor executes intructions on clock edges. In other words we can say that when clock frequency rises, speed also increases, but the device should be capable of operating in that frequency. (That details can be obtained from datasheets, CAD Tools report files etc).
Now in counter designs, clocks are important. The counter increments or decrements in active or level of clocks.
If I understood right your question...
Clock gives pulses. Depend on the Hz Of your clock you have the relatively speed.
For example, if you have a counter with a clock at 50Hz then your counter will increase/decrease faster than a counter with a clock at 20Hz.
In electronics and especially synchronous digital circuits, a clock signal is a signal used to coordinate the actions of two or more circuits. Think about synchronous. But this is very wide definition. Usually clock is the fastest signal in your circuit and operations of your circuit ( specially state devices... flop and latch) depends on the clock. e.g. If you have a flop then its output changes once clock arrives ( edge triggered ).Circuits using the clock signal for synchronization may become active at either the rising edge, falling edge, or both edges of the clock cycle.
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