Max HP (x): Renee's maximum hit points. Note that this doesn't tell you her current hit points.

Max MP (x): Renee's maximum magic points.

Main Weapon Attack (x): The general strength of Renee's physical attacks. This doesn't take into account what weapon she's attacking with.

Defense (x): Renee's ability to withstand damage. There's no numerical indication of how much damage enemies inflict, so it's hard to tell this stat's exact relationship with how much damage she takes.

Critical Rate (x%): The chance that any of Renee's attacks score a critical hit, which generally deal double the damage of her usual weapon attack.

Critical Damage (x%): The damage of any critical hits Renee inflicts is altered by this percentage.

Drop Rate (x%): All enemies have a base chance of dropping an item when killed; this stat increases the chance of that happening. I don't know if this applies to all the possible items an enemy can have or just the non-rare ones.

Normal Attack Damage (x%): When Renee attacks with one of her weapons, the damage is altered by this percentage.

Weapon Skill Damage (x%): When Renee attacks with a weapon skill (one of the weapon attacks with a button sequence that you buy from the Talent Tree), the damage is altered by this percentage.

Subweapon Damage (x%): When Renee attacks with a subweapon - a spellbook, scroll, wand, or staff - the damage is altered by this amount. I don't know if this percentage alters any non-damage effects of her spells.

HP Regeneration (x): After a set period of time, Renee's current hit points increase by this amount. Note that if this number is negative, her hit points will decrease instead, and the effect stops when she's at maximum. This stat can only increase through equipping items.

MP Regeneration (x): After a set period of time, Renee's current magic points increase by this amount. Note that if this number is negative, her magic points will decrease instead, and the effect stops when she's at maximum.

These stats aren't recorded anywhere you can see aside from any equipment or Talents that grant them. I think I've managed to figure them out based either on intuition or actual testing, but I'm pretty sure I've got these defined correctly.

[Weapon] Attack (+x): Whenever Renee is wielding the weapon listed in the stat, her attack rating is altered by this amount. This change isn't reflected in the "Attack" stat on the Talent Tree screen, nor are the Attack values for each different weapon type tracked separately anywhere.
Applicable Weapon Types: Blade, Book, Dual Dagger, Greatsword, Scroll, Scythe, Staff, Sword, Wand, Whip.

Contact Damage (x%): Whenever Renee takes damage from running into an enemy, the damage is altered by this percentage. I don't know when it's applied in the damage calculation.

[Element] Damage (x%): When Renee deals any damage that's classed as a specific element (e.g. casting a spell from the Book of Pyro, an attack from the Holy Whip), that damage is altered by this percentage.
Applicable Damage Types: Anemo, Geo, Hydro, Lux, Pyro, Soul.

Damage Received (x%): Whenever Renee takes damage, the total is altered by this percentage. I don't know when it's applied in the damage calculation, and I'm assuming it applies to all sources of damage.

Dew Gain (x%): Whenever Renee gains Dew, the total amount she gains is altered by this percentage. I don't know whether this percentage is applied to each individual Dew orb or if it's applied to all Dews she gains in a set period of time.

Experience Gain (x%): Whenever Renee gains experience, the total is altered by this percentage.

Final Damage (x%): Whenever Renee deals damage, the total damage is altered by this percentage after every other relevant stat is applied.

Healing Efficiency (x%): When Renee uses one of her Glyphs to heal herself, the healing she receives is altered by this percentage. Note that, as far as I can tell, this only affects healing received from using glyphs, and doesn't alter healing from any other source, such as potions, healing spells, HP Recovery, and HP Regeneration.

HP Recovery (x%): If Renee is equipped with an item that allows her to gain HP after a specific trigger (e.g. Ring of Bravery), the total amount of HP gained when this action is triggered is altered by this percentage.

MP Cost (+x): When Renee casts a spell, the amount of MP she has to expend to cast it is altered by this amount.

MP Recovery (x%): If Renee is equipped with an item that allows her to gain MP after a specific trigger (e.g. Necklace of Bravery), the total amount of MP gained when this action is triggered is altered by this percentage.

Physical Resistance (x%): When Renee takes damage from a non-elemental source, the damage is altered by this percentage. I don't know when it's applied in the damage calculation.

[Element] Resistance (x%): When Renee takes damage from an elemental source, the damage is altered by this percentage. I don't know when it's applied in the damage calculation.
Applicable Damage Types: Anemo, Geo, Hydro, Lux, Pyro, Soul.