Constitution represents the health and stamina of a character. High constitution increases the number of hit points a character has (affecting how much damage they can take), and this makes it important for everyone, but especially so for fighters. If constitution ever increases, hit points increase retroactively as well. Spellcasters also need strong constitution to keep their spells from being interrupted during combat.
The constitution modifier is added to all fortitude saving throws and to the hit points gained each character level (subject to a minimum of 1 hit point per level). Furthermore, the constitution modifier is added to the concentration skill.
Bonus hit points from constitution are added "underneath" a character's rolled hit points. That is, damage is taken first from the rolled hit points, then from the bonus from constitution. Thus, a creature with few hit points may be killed by a reduction in constitution. For example, if a level 4 character has been reduced to 3 hit points, then reducing that character's constitution modifier by 1 will immediately remove 4 hit points from the character's maximum and current hit points, leaving the character dying with -1 hit points (unless the above minimum comes into play). In a situation like this, experience points (if any) are awarded to the last character to injure the victim, not necessarily the one who caused the reduction in constitution.