Special attacks are unique attacks that can only be performed by certain weapons. There are many types of special attacks, from temporary boosts in stats, to strikes dealing extra damage.
There is an ability that you can place on your Action Bar that, when you have a weapon that has a special attack equipped, will allow you to activate the special attack. If you click on the icon, then your character will initiate a special attack and use up an amount of adrenaline. If you are in the legacy combat mode, click the special attack bar on the combat styles interface.
Note that some special attacks require two weapons to be equipped: a main and an off-hand weapon.
Different special attacks use up different amounts of adrenaline/your special attack bar. If you do not have enough adrenaline, or your special attack bar is not filled enough, for your weapon's special attack you won't be able to use it.