What is "attack power normalization"?

Instant attacks are somewhat complicated. They're calculated based on weapon damage and attack power bonus. Since 1.8, the following weapon speeds are assumed for the attack power bonus:

Daggers: 1.7
Other one-hands: 2.3
Two-hands: 3.3

So, weapon speed no longer matters for instant attacks (namely overpower, whirlwind and MS), but weapon damage still does - this still makes slower 2h weapons superior to faster ones, just not by such a large margin. Bloodthirst is an instant attack as well, but doesn't rely on weapon damage, so there is no AP normalization at work for that one.

The formula for the average damage of 2h instants goes like:
Damage = (Weapon Speed * DPS) + (3.3 * (Attack Power / 14))