The number noted here is the eidolon’s base total armor bonus. This bonus may be split between an armor bonus and a natural armor bonus, as decided by the summoner. This number is modified by the eidolon’s base form and some options available through its evolution pool. An eidolon cannot wear armor of any kind, as the armor interferes with the summoner’s connection to the eidolon.
So the Eidolon has an armour bonus, and the summoner decides how much of that is armour and how much is natural armour. However, it seems to me that there is no reason you would ever want to use any of this bonus as armour rather than natural armour.
Methods for improving natural armour bonus usually stack with existing natural armour; methods for gaining armour bonus do not - Mage Armour does not stack with an existing armour bonus, the Eidolon cannot wear real armour to be enchanted with an enhancement bonus, etc. Bonus used as armour is effectively wasted while the Eidolon is under the effect of Mage Armour (and when should it not be?) but natural armour is always useful.
Further, I am not aware of any difference in the way natural armour and regular armour functions which would make it desirable to have armour instead of natural armour. In fact, natural armour is sometimes at an advantage, i.e. Brilliant Energy weapons ignore armour but not natural armour.
Is there ever any situation where it would be advantageous for some of an Eidolon's armour bonus to be armour instead of natural armour?