Attributes and Stats.

These attributes contribute to the "real stats" or stats used in battle

Strength 
(Also called Power) - Adds to your Physical Attack and Physical Defense
At level 9, each point of Strength adds 4 points of Physical Attack and 1 point of Physical Defense

Armor 
(Also called Defense) - Adds to your Physical Defense and Magical Defense
At level 9, each point of Armor adds 4 points of Physical Defense and Magical Defense

Intellect 
Adds to your Magical Attack and Magical Defense
At level 9, each point of Intellect adds 4 points of Magical Attack and 1 point of Magical Defense

Endurance 
Adds to your maximum HP. Each point of Endurance adds 20 to your maximum HP.

Charisma 
Directly increases your Troop Count at a 1:1 ratio

Battle Stats 

Physical Attack 
Represents the damage you deal in battle with physical attacks (Knight and Archer)

Physical Defense
Subtracts 1 Damage per 2 Pdef points from the damage you take from physical attacks, down to a minimum of 10% of the Attackers Patk rating

Magical Attack 
Represents the damage you deal in battle with magical attacks (Mage)

Magical Defense 
Subtracts 1 Damage per 2 Mdef points from the damage you take from magical attacks, down to a minimum of 10% of the Attackers Matk rating. 

Critical 
Your chance of a critical hit (1.5x?) is based on your Critical statistic. It seems to be approximately 0.04% per point in critical; the formula might be (1-0.9995^critical score)*100%.

Block 
Your chance of a dodge (damage reduced by some percentage) is based on your Block statistic. The formula is most likely the same as for Critical.

HP 
Your character's health. When this reaches 0, you're out of the battle.
Besides Endurance bonuses and direct HP bonuses from equipment, there appears to be a base HP amount, possibly based on level and class:

Level 27 knight had 432 (360 before 20% bonus)
Level 28 knight had 444 (370 before 20% bonus)
Level 30 mage had 410
Level 31 archer had 480 (400 before 20% bonus)
Level 31 knight had 504 (420 before 20% bonus)
Level 32 mage had 530
Level 32 archer had 564 (470 before 20% bonus)
(Roughly 90+10*level?)

Troop Count 
The maximum number of recruits you can bring with you into battle. This stat has no effect in multiplayer dungeons, since you can't bring recruits there.
The number of troops you have with you determines your troops' hitpoints. (Formula is: unit HP × your troop count / 200), so, for example, i have 751 knights (2906 × 751 / 200)=10912 HP. Troop count has no effect on the damage your troops deal.

Battle Rating 

Your battle rating is determined by adding all of your battle stats together, but with Magical Attack multiplied by 1.05 (and rounded down), and HP divided by 5 (and rounded down). This value is shown to other players, and is intended to give a rough idea of how powerful you are.

Equipment Rating 
The equipment rating for a piece of equipment follows a simple equation:
Eq. Rating = Stat(s) modified rating + Bonus(es) rating

The stat(s) modified rating is the simplest part of this, and works as follows: 1 point for each ATK/DEF, and 1 point for every 5 HP. That means that an equipment which adds 100 ATK would have a base rating of 100, while an equipment which adds 100 HP would have a base rating of 20.

The bonus(es) works a bit differently. There are two types of equipment bonuses: attribute bonuses and battle stat bonuses. The former provides smaller numerical boosts than the latter. For the attribute bonuses, the bonus rating goes: 1:8 for Power, Intellect, and Armor; 1:4 for Endurance and Charisma. In other words, if an equipment provided +15 Power, +8 Armor, and +10 Endurance, the bonus rating would be 224 (15*8 + 8*8 + 10*4). Note that Armor is called Defense by these bonuses.

The battle stats bonus works in a similar manner, and will be presented in large numbers. For PATK/MATK/PDEF/MDEF/CRITICAL, the bonus works in a 1:2 ratio; that is to say, if a bonus gave +70 MATK, the battle stats rating would be 140. HP works in a 1:(1/5)*2 ratio, meaning the HP stat is first divided by 5, rounded down, and then multiplied by 2. If an equipment bonus gave +143 HP, the battle stats bonus would be 56 [ (143/5) = 28.6, rounded down to 28, and then 28*2 = 56) ]. Note that BLOCK gives zero equipment bonus rating.

Let's look at an example equipment rating. A piece of equipment modifies PATK by 165 and has the bonuses +13 POWER, +20 ENDURANCE, +83 PATK, +70 BLOCK, and +164 HP. It's equipment rating would be:

Stat modified: 165 PATK --> 165

Bonuses Rating: 13 POWER, 20 ENDURANCE, 83 PATK, 70 BLOCK, 164 HP -->

13 * 8 + 20 * 4 + 83 * 2 + 70 * 0 + floor(164/5) * 2 = 414

So the total equipment rating would be: 165 + 414 = 579

Note that gems are included with the enchanted equipement rating; this appears next to the equipment rating in parenthesis. The extra effect from soul engraving does not affect the equipment rating.