Strength represents your physical power. It increases melee damage and unlocks items and abilities.
Toughness* describes physical conditioning. It permanently increases life energy and unlocks items and abilities.
* - "Toughness" is probably misstranslation of "constitution".
Improving dexterity increases ranged damage and unlocks new abilities and items.
Depending on your faction, increasing intelligence permanently increases mana, or PSI power and unlocks new abilities.
Cunning influences social skills and unlocks certain abilities. For Outlaws, it increases chem capacity.