@What are companions?
Companions are any follower, minion, or pet obtained through items, buffs, or skills. You can easily identify them by them having a health bar. Orbital enchants etc are not considered companions.
@What stats affect my companions?
Your companion's Damage and Health is directly based on your own Damage and Health stats, by the indicated percentages on the skill/item. This is then multiplied by the "Companion Health" and "Companion Damage" stats. Companions also use your Elemental Damage, Resistances, Crit Chance, Crit Damage, Overpower, and Movement Speed stats.