O.o never had one of this thing happen to me (2nd paragraph)... but sounds really cool.The world artifact power drops are actual items that can be activated and applied to the artifact of your choice by clicking the item then selecting the artifact you wish to apply it to. There are certain milestone quests while levelling that also award these items. These items are ranked by color/rarity like regular gear drops. Green = Uncommon, Blue = Rare, Purple = Epic, etc. Each rarity level awards more AXP than the previous. The upshot of this system is that you can use your main spec to grind AXP items for your offspec artifacts.
In addition, there are certain times or locations out in the world where just walking through will initiate a scripted sequence where you are automatically awarded a bit of artifact XP to your equipped artifact. I cant say how common these are, as ive only seen one thus far. For example, theres a spot in Val'Sharath where i was walking to a quest objective on my Frost DK where the spectre of the Lich King appeared in the middle of a ruined path and did a short RP monolog after which i was awarded 50 AXP directly to my equipped swords.