Both run simultaneously, but only one is in effect.
Effectively you reset the duration of the spell.
Most spells create a specific effect, such as an armor class bonus or an enhancement bonus. Effects of the same name don't stack, so casting "Cat's Grace" twice will not stack. However, both spells would be active so the effects would overlap in rounds.
If there is any spell that does stack with itself, I can't think of it, but someone else might be able to.
