Constitution represents your character’s health and stamina. A Constitution bonus increases a character’s hit points, so the ability is important for all classes.
You apply your character’s Constitution modifier to:
Each roll of a Hit Die (though a penalty can never drop a result below 1—that is, a character always gains at least 1 hit point each time he or she advances in level).
Fortitude saving throws, for resisting poison and similar threats.
Concentration checks. Concentration is a skill, important to all spellcasters, that has Constitution as its key ability.
If a character’s Constitution score changes enough to alter his or her Constitution modifier, the character’s hit points also increase or decrease accordingly.
This is commonly the highest stat for Barbarians or other melee front line classes, but should never be the lowest stat for any character. It is vital for every role as it reflects your Hit Points, which are important for not dieing.
For more uses of Constitution see this thread over on the WoTC boards. X Stat to Y Bonus