You are activating the skill that provides counters.
You can then see the counters as a "buff" for your character.
Depending on the counter it can increase in number on certain circumstances or it lowers it number and has a certain effect when do so. For example extra damage when hitting an enemy (thousand cuts) but losing 1 counter. Nature counters, to give another example, can be build up by different skills and the number of nature counters you have can buff some other skills in it's power. You can get counters not only by activating skills but have a passive buff that says you get "X (melee/nature/lighting..)counters" by doing different stuff, mostly damaging foes.
Counters decrease after time spent not using them.