The primary attribute describes the most important ability statistic of the character's class. When a player creates a character, the player improves the character’s survival if the highest roll is placed upon the character’s primary attribute.
For example, a player has decided to be a fighter. The primary attribute for fighters is strength. A fighter’s minimum strength is 9. Under the rules, the player is free to assign any stat above 9 to their strength in order to meet the fighter's requirements — but a fighter with a mere 9 strength would be a poor fighter. Placing the highest of the player’s six rolls would be wiser.
So the primary ability is a guideline for the player when choosing stats. It's not a requirement — but often it's good policy.
Strength is the primary attribute for assassins, fighters, paladins and rangers. Wisdom is the primary attribute for clerics, druids and monks. Intelligence is the primary attribute for illusionists and mages. Dexterity is the primary attribute for thieves. Charisma is the primary stat for bards.