What do each of the stats (HP, MP, etc...) do?
Any of these stats can be renamed for your game. You can make stats hidden on a per-hero basis in the Hero Stat Editor.
Each stat has a current, maximum, and base value. Read the Permanent Stat-Boosters article for background information about that.
Health Points. You lose these when you get hit by enemies in battle. When you run out, you die.
Magic Points. Consumed when you cast a spell. When you run out, you cannot cast any more spells. There is also a second MP system, called Level MP; see What are Level MP based/FF1 Style spells?. A hero always has both regular and Level MP, but the Level MP is hidden unless the hero has spells that use it.
Attack power. Normally determines the damage you do when you hit the enemy. (Although many other factors affect battle damage; see How is damage calculated?)
Accuracy. Affects whether or not you miss your target. See also How is the attack dodge rate calculated?
Defence. Reduces the amount of physical (non-magical) damage done to you. Subtracted from the enemy's Atk stat.
Dodge. Affects whether or not you dodge the enemy's attack. See also How is the attack dodge rate calculated?
Magic power. Normally determines the damage your spells/skills do.
Will Power. Reduces magical damage. Subtracted from the enemy's Mag stat.
Speed. For active-time battle mode, this affects how fast your ready-meter fills up. This should usually be within the range of 10-30. A higher number leads to quicker turns.
For turn-based battle mode, this affects turn order. The hero or enemy with the highest speed stat will attack first.
Counter. Does nothing. This was originally intended for counterattacks, but was never implemented as such. You can use it for any purpose without worry about it being used for a builtin purpose later.
MP Modifier. A percentage by which your MP consumption is reduced. A high MP~ lets you cast more spells. Eg. if this stat is set to 50, spells will cost half as much MP.
Extra Hits. Causes attacks to have a random chance of being be duplicated. For example, a value of 2 means that the hero will hit between 1 and 3 times every time they do an attack (unless the attack is set to ignore the extra hits stat). A value of 5 means they will hit between 1 and 6 times. Use this sparingly-- nothing is more annoying that a game where every single hero and every single enemy randomly does up to 20 hits with every attack.
Note that the Extra Hits stat differs from an attack's Number of Hits, which is not randomised: the full Number of Hits occurs, plus an additional number of hits between zero and the attacker's Extra Hits.