Counterstrike is an ability that gives a chance for your pet to deal a little extra damage if they dodge the opponent's attack. Not to be confused with an elemental attack combo such as Lightning Strike, Acid Spit, or Fire Breath, which deals 150% of normal attack damage when using Bite.
Arguably the elemental attack combo is rarer, since both the genes it requires are recessive to nearly every other, while Counterstrike requires a universally dominant gene, making it easier to breed. Counterstrike comes from the combination of Quickmind and Agile Paws, while elemental attack comes from Fire Gland/Acid Gland/Steel Beak and Spitting Muscle/Electric Gland, depending on species. (Also, lykos only require one gene, Ice Breath, to gain elemental attack, making it the easiest to get.)
Personally, the presence of a combo ability does not dramatically increase a pet's value to me unless its other genes are good as well. Some people put more stock in them than others.