Touching Spirit Bear has both a literal and a figurative meaning for the novel's protagonist, Cole Matthews. Cole does actually touch Spirit Bear when he comes to the island—you know, when he tries to kill the bear and ends up grabbing a handful of his fur. This results in a near-death experience for our main dude.
There's more to the title than just a shout-out to that one (misguided) physical touch, though. Through Cole's near-death experience, he learns a lot about himself and how he wants to live out the rest of his life. Being mauled by Spirit Bear ends up being the best thing that ever happens to Cole because it forces him to confront his mistakes and the way he's been living his life. It sets in motion the desire to change his life for the better.