Constitution represents the health and stamina of your character.
Some of the things which a character's Constitution score affects are:
Hit Points- Whenever a character gains a level, they add their Constitution modifier to their Hit Die to determine how many Hit Points they gain. Note that a character will always gain a minimum of 1 Hit Point per level, regardless of their Constitution score.
Fortitude Saving Throws- Characters add their Constitution modifier to Fortitude Saving throws, used to resist poison and similar threats.
Constitution is important for everyone, but especially for fighters and barbarians. If Constitution ever increases or decreases, Hit Points increase or decrease retroactively as well. Constitution is also used for the Concentration skill, so spell-casters also need a strong Constitution to keep their spells from being interrupted during combat.