"The Patronus is a kind of positive force, a projection of the very things that the Dementor feeds upon - hope, happiness, the desire to survive - but it cannot feel despair, as real humans can, so the Dementors can't hurt it." - Remus Lupin
See the full-sized artwork here. [external link, opens in a new window]
Despite its title, this card does not necessarily mean superhuman feats or bulging muscles. Strength here is not showy or flashy--it is a quiet inner strength that provides support through hard times. This card contains patience, composure, and compassion. It serves as a reminder not to despair or give up.
As Professor Lupin points out, the positive magic of a Patronus certainly matches the properties of Strength. However, as a part of Harry's life "journey", it serves a part even bigger than a simple protective totem. Through his repeated training to summon his Patronus, Harry learns to face and overcome his deepest fears, something not even many experienced wizards can accomplish.
Traditional imagery for this card depicts a woman taming a lion, symbolizing inner strength overcoming the wild, bestial instincts. Naturally, here Harry is seen "taming" the true form of his Patronus.