With this type of proficiency, a character can spend time and effort learning how to use their armour more efficiently.
While this doesn’t provide a bonus to Armour Class, it can help to offset the hefty encumbrance penalties of heavier armour types.
Armour types are classified as light, medium, or heavy. Proficiency in one type grants this benefit for all armours in that weight category.
A character who spends a weapon proficiency slot becoming acquainted with a type of armour gains the special benefit of not suffering a reduction in movement rate when wearing that armour.

You can take a proficiency in the following:

Medium Armour: When wearing medium armour, your movement rate is 12 instead of 9.

Heavy Armour: When wearing heavy armour, your movement rate is 9 instead of 6.
If you are wearing a masterwork suit of heavy armour, and you have the heavy armour proficiency, your movement rate is 12, as the benefit from the masterwork quality stacks with this proficiency.

Larceny Abilities:

Any character that has Larceny abilities can invest in armour proficiency for Leather or Studded Leather Armour.
This reflects the character taking time to learn how to compensate for the armour’s restrictive movement, or even making small adjustments to the suit to improve flexibility and maneuverability.
Doing so will reduce the Larceny penalties associated with that type of armour by as much as 15% in all abilities, but never below 0%. The proficiency will never apply a bonus to the ability. The character needs to spend a slot in each type of armour. So having a slot in Leather Armour, will not automatically cover Studded Leather Armour as well.

Arcane Spellcasters:

For Arcane spellcasters, armour is usually off limits. The weight, bulk, and construction simply makes wearing it impractical and too cumbersome.

Investing in Armour proficiency, allows the arcane spellcaster to wear Light Armour and still cast their spells as if not wearing any.

• The first slot buys the caster the ability to use Padded armour, or masterwork Leather.
• The second allows the use of Leather armour, or masterwork Studded Leather.
• The third allows the use of Studded Leather, or masterwork Chain Shirts.
• The fourth and final slot allows Chain Shirts, or masterwork Chainmail.

No more than 4 slots may be invested in this way.

In addition to this approach, a character may also attempt to find exotic suits of armour that allow spellcasting. See here: Armour