The book lists the difficulty for lightly wounded and critically wounded characters. It says that any character with a critical wound is critically wounded. However, the Resilience check only seems to grant a benefit against critical wounds; it allows you to turn one critical wound into a regular wound. So, what is the point of making a Resiliance check when you are only lightly wounded?

From the next sentence: "He also recovers an additional number of normal wounds equal to any boons generated."

As crasher said, the check allows for some additional Wounds to potentially be healed.