It's basic 'Want vs Need'. The Want is a stated goal the character wants to achieve which is the motivation that drives the initial plot, and the Need is what the character ultimately needs to do in order to grow and develop. In most Western film, television, and literature this dynamic culminates in the character ultimately choosing and embracing Need over Want in the climax of the story, leading to the catharsis of the character's emotional arc.
Fir example: In Up, Carl Fredrickson *wants* to be left alone to grieve for his wife. To accomplish this he ties balloons to his house and flies it to Paradise Falls where they'd always planned to travel to. He *needs* to stop grieving and live his life. This emotional conflict is concluded when, during the climax of the story, Carl lets the house, the physical embodiment of his grieving for Ellie, go.
In Samurai Jack, Jack *wants* to return to The Past and undo the future that is Aku. Jack goes on a quest to find the means to accomplish this. Jack *needs* to forgive himself, accept what happened, and move on with his life and focus on The Future. The people Jack encounters and helps on his quests, and the lives he changes for the better, help him accomplish this. That story needs to and should have ended with Jack choosing to stay in The Future and embrace his new life and the friendships and love he's found there. It didn't, and is thus, for many viewers, an unsatisfying ending.