So if I had level 20 resist lightning with a dream on, would that level 15 holy shock receive the bonus of the resist lightning synergy?

Aura When Equipped, Charges, and Chance to cast skills receive bonuses from their respective synergy skills.

http://wiki.theamazonbasin.com/index.php/Skill

"Skills used receive passive bonuses including synergy bonuses, but do not apply them." What does that mean though?

They benefit from synergy skills but do not act as synergy skills.
Synergy skills require skill points to apply their synergy bonuses to other skills.

Items, not skill points, are the sources of Aura When Equipped, Charges, and Chance to cast skills.