Here's the adjustment:
"Spell failure chances for armors and shields made from mithral are decreased by 10%, maximum Dexterity bonuses are increased by 2, and armor check penalties are decreased by 3 (to a minimum of 0)."
So for a breastplate, you would go from
+3 Max Dex bonus, –4 Armor check penalty, 25% spell failure chance
To
+5 Max Dex bonus, –1 Armor check penalty, 15% spell failure chance
As far as "medium" to "light", that is about the general game effects of the different categories of armor, described here: http://paizo.com/pathfinderRPG/prd/equipment.html#_armor.
The primary differences are that you can sleep in light armor without fatigue and that light armor does not reduce your speed. There are other differences, depending on class features (rogues can use evasion in light armor, but not medium, for example), but those are most common.
Note that mithral does not change the proficiency required for medium armor. You still have to have medium armor proficiency to wear a mithral breastplate without a nonproficiency penalty. ("Nonproficient with Armor Worn: A character who wears armor and/or uses a shield with which he is not proficient takes the armor's (and/or shield's) armor check penalty on attack rolls as well as on all Dexterity- and Strength-based ability and skill checks.")
Also note: while not relevant for this character (since clerics usually have medium armor proficiency), you can make it possible for a character to use a mithral breastplate without needing the proficiency.
As Gwen said, the penalty for using an armor you don't know how to use is to apply its ACP to your attack rolls. But if ACP is 0...the penalty is 0.
Mithral, as it has been stated, reduces ACP by 3. The trait 'Armor Expert' further reduces it by 1. I think there is also the 'comfort' enhancement that does the same thing, but the trait is easier. Anyway, together, you reduce 4 points of ACP, meaning anyone with a trait to spare (and not restricted like a wizard or standard monk) can grab a mithral breastplate.
