Each character has a rating for seven essential attributes and two variable. The former, described more fully below, are rated from 1 to 25. Their values can be changed in several ways: temporarily with magic, permanently by donating money to the Temple or levelling up, and also by equipping accessories; with this latter method, you can boost your stats above 25; the absolute maximum is about 33.
The variable attributes are HP and MP, representing (as usual) the character's health and magical power; the absolute maximum value for each is 9999. Both can be recovered with items, by making a tiny donation at the Temple, or by staying at the Inn; HP can also be recovered by resting on save points or with the Restore Lute skill. The maximum values for each will increase on levelling up, or on donating a large sum to the Temple, by an amount determined by the character's sex, level, and job.
A word needs to be said about these job-related changes. The amount in each case is not absolute: there's a fairly random element involved. If you save before levelling up, you can reload and try again if the results aren't to your satisfaction. Note that the random seed is only changed when you change screens (for this purpose, the whole town counts as a single screen), so this takes patience.
"Raises weapon hit rate in battle."
When your accuracy is low, you'll often only do 1 damage even on enemies with low dexterity.
"Ability to evade enemy attacks."
Likewise: the higher your dexterity, the greater the chance that even accurate enemies will barely scratch you.
"Raises magic power and evasion."
Note the latter: even non-magic users will benefit from greater intelligence. Besides, frankly, you'll probably want all your characters to be able to use healing magic.
"Ability essential for opening things like locked doors."
This directly affects the speed at which the numbers change. You only need it high on one character, whom you should put in the lead when you want to pick a lock.
"Determines movement range and AP in battle."
This is very useful (it lets you get the first hit in with melee weapons), and is essential if you want to equip heavy armour and still be able to move.
"Determines time taken to recover status and physical strength."
This appears to affect how long status ailments last, and how much HP is restored when you rest at a save point or use Restore Lute.
"Depending on this value, good things may happen..."
It is unclear how Luck is used. It might be that it affect your chances of scoring a critical hit, or of finding treasure. It also seems to be necessary for some of the better jobs...