In Advanced Paper Mario, each character has the following statistics:
Statistics which can be raised with Star Pieces: HP, FP, BP.
Statistics which depend on skills and equipment: Power, Armour, Resistance, HP Regen, FP Regen, Evasion, Critical, Action.
Upon creating a character, you pick a Base Class. You start with 10 HP, 5 FP and 5 BP. Your character may also have Starting Equipment as well, listed on their character page.
You can advance your character by leveling up by winning battles or via other means. Each level up awards one Star Piece, which you can use to upgrade your HP, FP or BP, or alternatively spend to unlock new Skills for your character (based on your Class).
Skills are what makes any class. There are two main skill categories, Active and Passive. Active skills can be used by spending an Action to use it, and often require a target. To contrast, Passive skills are often always in effect, or otherwise trigger automatically.
Any given skill may have a variety of properties, listed here: Name - The name of the skill. Type - The type of the skill. Active Types include: Active (Requires 1 Action to use), Instant (Usable without using an action) and Toggle (Usable without an action, causes a passive effect while toggled on, often with an EOR cost). Passive Types include: Passive (Persistent effect), Permanent (Persistent effect which can't be negated in any way) and Triggered (Effect which triggers under a specific condition.) Use - What's required to use the skill. Some skills have no requirement outside of having it. However, skills commonly have a FP Cost which must be paid when using a skill, and a skill might consume your partner's action, or also require you to have a Hammer equipped in order to use it, for example.
Characters can equip a variety of equipment. The type of equipment a character can equip is dependent on their class, but all classes have the same three equipment slots: One Weapon, one Armour and one Accessory.
Weapons commonly boost a character's Power, Armour commonly boosts a character's Armour and Resistance, and Accessories have a variety of uses. Additionally, all equipment types may come with additional Equipment Skills, special skills which are unlocked for as long as you're using the equipment.
A table of Base Classes and what they can equip goes here. A table of Partners and what they can equip might also go there, though ATM I'm thinking of Partners just having accessories (which may or may not have type limitations)
Along your adventure, you can gain Partners who will aid you in battle. Partners share your HP, BP and FP, but have their own Power, Critical and Action stats, and may equip items independently of you. In addition to using a skill you're able to use, you can also command your Active Partner to use skills during your turn.
Partners have their own Skills, and you can upgrade your partner by unlocking new skills using Star Pieces you gain by leveling up. If you ever dismiss a partner, the Star Pieces are refunded.
You can have up to two partners with you at any one time, but only one Active Partner in battle. You or your Partner may use an action to switch your Active Partner with your Reserve Partner.
Badges are additional skills you can equip using your BP. A badge can be equipped to either you or your partner, but you share the same BP. The total BP cost of all your equipped badges cannot exceed your BP.
Some badges have other prerequisites to equip or use, such as being a specific class, or wielding a specific weapon type.
A character can hold an inventory of up to 10 items. Most items can be used in battle, to great effect, but are consumed on usage. Badges and Equipment are also forms of Items, but are stored in a separate, unlimited inventory.
All items (Including Badges and Equipment) have an Item Type, Rarity and Requirement.
Requirements are prerequisites to wield the badge or equipment. A badge for instance might require 5 BP, or a specific class.
Item Types are vast, but you can check out the full list on the main items page.
Likewise, Rarities are also vast, but you can check out the list on the main items page.