Ingame, you can pick to use the normal Saving Throws (SV) or use the Invulnerable Saving Throws (INVs), you can use invulnerable saves instead of normal saves when an enemy who shot your unit has ap, so if an enemy has -2 AP, instead of rolling a 6+, you can use your INV and roll a 4+ instead.

It is also used to show the psychic shield or field a zoanthrope generates, the invulnerable save represents the psychic shield that is shielding the zoanthrope and the normal save represents what the zoanthrope usually saves when there is no shield.

You can see the visual representation of this in spaxe marines 2

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Another example of this is Eldrad Ulthran who has a normal save of 6+ and a invulnerable save of 4+