Cover comes in three levels:

Minimal: +1 to defend.
Partial: +2 to defend.
Total: +3 to defend against AoE attacks. Other attacks must break through.

What level of Cover an object provides depends on its shape and Size.
Generally, an object with a Size one lower than the character is Minimal, equal is Partial, and larger is Total.

Total Cover also provides Concealment.

To resolve attempts to attack through cover you first determine if the cover is Permeable or Destructible.

Permeable cover includes energy shields, solid objects with gaps or holes, or machinery that isn't of uniform Resilience.
Permeable cover can be fired through, it gives a bonus to Resist Damage equal to its Resilience.

Destructible cover is solid, mostly uniform, objects.
Destructible cover can be destroyed and provides protection to the target behind it.
Deal Damage to the cover (the TN based in its resilience):

Critical Successes break through, apply the same roll to the target.
Successes break through, apply the same roll with a -2 penalty to the target.

Breaking through Destructible cover reduces it's level by one:
Total to Partial, Partial to Minimal, Minimal to None.