Vitality is a measure of how much punishment and damage a character can withstand before they begin dying. Your Vitality increases every time you level up in a class, and is calculated as such:
At first level, you have Vitality equal to [Class Starting Vitality]+[1d12]+[Constitution Bonus].
Every level after the first you roll your Vitality Dice, which is [1d12]+[Constitution Bonus] and increase your maximum Vitality by that much.
When you increase your Constitution Bonus by 1, you gain 1 Maximum Vitality per Character Level.
Similarly, when you decrease your Constitution Bonus by 1, you lose 1 Maximum Vitality per Character Level.
When you take damage, your Vitality is reduced by the amount of damage taken, to a minimum of 0. See: Rules for Death.