What is 'Cultural Armor'?

Cultural armor is indeed different for each race. The differences aren't just cosmetic, as each race's set of armor has different set bonuses.

Race        Major Bonus     Minor Bonus 1     Minor Bonus 2
Asura    Condition Damage     Vitality           Power
Charr          Power        Critical Damage    Precision
Human          Power          Precision      Condition Damage
Norn           Power          Vitality         Toughness
Sylvari  Condition Damage     Precision        Toughness

The armor is roughly analogous to Prestige Armor from Guild Wars 1, though that armor was entirely cosmetic. Because of its higher cost, it's a way to reward players who have had the time/resources/money to acquire that much gold to afford the items.

As of this moment, because it's so early in release and the Trading Post is still disabled, it's difficult to know exactly how this armor compares, stats-wise, to the crafted Legendary sets in the game, though it is almost certainly better than the random mob drops.