The Patience Score determines the number of times that your character can retry a specific skill or task before he gives up. Once your character has attempted a task a number of times equal to his patience score, he cannot retry again until significant time has passed or something about the situation has changed. Of course, patience only applies in situations where your character has the opportunity to retry the task. Some tasks cannot be retried, such as recalling knowledge (your character either knows it or doesn't), while others may have adverse effects to failure (such as setting off a trap your character is attempting to disarm).
Your character's Patience Score is dependent on his Wisdom, and can be looked up in the table to the right. Feats and other abilities may add other bonuses to this score.