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a fear effect so its total magnitude is amplified.
https://en.uesp.net/wiki/Skyrim:Fire_Damage
https://en.uesp.net/wiki/Skyrim:Illusion
You cannot have any rank in the 'Intense Flames' perk without at least 1 rank in Augmented Flames, so part of the info you got is wrong (the part about having 'zero ranks in Augmented Flames'). Having 1/2 Augmented Flames + Intense Flames however will add a flat 12.5 fire damage to spells (on top of what is normally added by the perk), and having 2/2 Aug Flames + Intense Flames will add a flat 15 damage.
The spell where this effect is most pronounced is probably the Ignite spell, which you can get from Ahzidal's Ring in the Dragonborn Expansion. It normally deals '4 damage per second for 15 secs for 60 damage total', or '6 damage per second for 15 for 90 damage total' if you have 2/2 Augmented Flames. However, with Augmented Flames 2/2, Intense Flames, AND Aspect of Terror, this spell now deals 21 damage for 15 seconds for 315 damage total. That's a 5 fold increase in damage from only 4 perks!
Over at Uesp it was found out a few years back.