Statistics are numeric values which represent a monster's aptitudes and physical abilities. Every action performed in combat is affected by a monster's statistics.
Hit Points
A numeric representation of a monster's remaining life force. HP is reduced as damage is taken, and when all HP is removed a wild monster will die. Tamed monsters are protected from death by the glyph of empathy, and are instead reduced to dying status. HP can be restored in or out of battle by restorative items and healing abilities. HP value is equal to one half a monster's constitution times its level plus base HP. Or (1/2 CON*LV)+Base HP.
Magic Points
Casting magic requires an amount of spiritual energy, and every spell will reduce a monster's MP count by a specific amount. MP regenerates on its own over time, but can be recovered instantaneously with items and abilities. MP value is equal to one half a monster's wisdom times its level. Or 1/2 WIS*LV
Attack Power
ATK is an important stat for physical attackers. Whenever a physical ability is used, ATK is multiplied by the ability's power rating and then divided by the target's DEF to determine damage dealt.
Defense Power
DEF is an important stat for all monsters, as it reduces damage from incoming physical attacks. Monsters with low DEF will need to be given armor if expected to go up against physical-based enemies.
Magic Power
MGC is the magical counterpart to ATK; whenever a magical ability is used, MGC is multiplied by the ability's power rating and then divided by the target's RES to determine damage dealt.
Magic Resistance
RES protects against magical attacks, and is as important as DEF in the reduction of damage. Monsters with low RES need to be given armor if expected to go up against magical-based enemies.
Speed
SPD determines how quickly the battle time gauge will fill, determining the order in which turns occur. Faster monsters will act sooner and more often.
Constitution
CON affects how much HP a monster has. As such, this is a very important stat for all monsters. HP increases by level are based solely on changes in CON.
Wisdom
WIS is very important for magic using monsters, but less so for physical based monsters. Wisdom affects how much MP a monster has. MP increases by level are based solely on changes in WIS. Physical abilities, and magical abilities granted by weapons use no MP, and monsters using only physical abilities can safely ignore WIS.
Other Statistic Related Concepts
Base and Growth
Every monster has a set of base statistical values and a set of statistical growth values. Base values (with the exception of HP) never change, except during metamorphosis. Stage 0 monsters have a total of 30 base stat points, Stage 1 monsters have a total of 50, Stage 2 monsters have a total of 70, and so on and so forth.
Upon leveling up a monster will receive a number of stat points, which the player can apply to a monster's statistics. The number of points received depends on the monster's metamorphosis stage; Stage 0 monsters gain 3 points, Stage 1 monsters gain 5 points, Stage 2 monsters gain 7 points, etc.
AP Attacks
AP Attacks don't use stats to determine damage; instead the ability's power rating translates directly into damage regardless of the attacker's ATK or the defender's DEF. This makes them very useful for monsters with low ATK or against enemies with high DEF.