Spell Points (sometimes called "SP") are used to upgrade a character's spells, making them more effective. This may involve lowering the spell's AP cost, increasing the spell's damage, amongst other things.
It is often beneficial to upgrade a single spell to provide one powerful attack, instead of spreading spells points out over a number of weak ones. However, not all useful spells are worth taking to their maximum level, so don't boost indiscriminately.
See Spell for more information about upgrading spells.
There are three ways to gain SP: