The Skill Bar contains all your currently equipped Skills.
The Skill Bar has 8 slots. According to the official explanation this is because "most skills come in the form of a ring to be worn on the character's finger, which is why one can take only 8 skills into battle."
To execute one of the equipped Skills you can click on its icon or press its corresponding key. Skills are always numbered 1 to 8 on the keyboard, unless you change their shortcuts (in this case, the numbers disappear).
Some skills will require you select a specific target before execution: either an ally, a foe, a pet or a spirit. Offensive skills and attacks may automatically select a valid target if one wasn't selected manually, as long as there is one available and Auto-Targetting is not disabled in the General Options panel (F11).
An upward arrow in the top right corner of the skill icon indicates that the skill is an Enchantment. A downward arrow in the same location indicates that the skill is a Hex.