I just don't understand the description "Ignores any stat changes in the Pokémon."
Unaware means the Pokemon completely ignores the effects of stat changes when calculating damage. Those changes are the standard ones you see from moves like Swords Dance. So if a Pokemon with a +2 Attack boost from Swords Dance attacked a Pokemon with Unaware, the stat boost would be excluded as if it wasn't there at all.
The Ability Unaware ignores all stat changes
Unaware ignores other Pokémon's positive and negative stat changes when calculating damage involving a Pokémon with this Ability. This means that damage dealt by a Pokémon with Unaware ignores the target's Defense and Special Defense stat changes. Likewise, damage dealt to a Pokémon with Unaware ignores the attacker's Attack and Special Attack stat changes.