From the outset, we know for sure that things aren't going to work out so well for the vast majority of Titanic passengers. So it's kind of (darkly) ironic that perseverance is a big theme in the movie.
Jack, in particular, is very big on never giving up, no matter how bleak things are looking—which is why he fights like mad to survive the sinking of the ship. Other people are tossing themselves off the side of the boat or hunkering down in their rooms and just going down with the ship quietly, but not Jack—he drags Rose around the ship trying to make sure they avoid going into the water as long as possible, and he gives Rose a pep talk about never giving up ever as they marinate in the freezing water, waiting for rescue.
And it's a good thing, since Rose has felt less able to push through life's difficulties. After all, she and Jack met when she was trying to work up the nerve to throw herself off the back of the boat. Ultimately, she gets the message and manages to survive the night of Titanic's sinking and live an amazing, adventurous, super-fulfilling life.
Cameron makes the movie go on an extra hour after Rose could have left in a lifeboat, but Jack still ends up dead, and Rose lives. His decision did nothing for the plot other than extend it.
Rose didn't end up dead when she opted to stay with Jack rather than go on the lifeboat—but she could have, and that willingness to stick with love over safety marks a big change for her character.
The Titanic's basically a floating melting pot of people from different countries, classes, and social backgrounds. This creates the opportunity for the very well-heeled Rose to meet a poor artist named Jack Dawson.
Many of the ship's richer passengers are total snobs—and, as such, uninterested in interacting with passengers who are different from them in any way. Rose's mother falls into that group, which is why she's not impressed when Rose strikes up a friendship with Jack.
And while basically everything else in the movie is tragic, we do get one big bright side: Jack and Rose prove that actual love and connection is way more important than money or status, and Rose's ultimate ability to break from class and convention is what enables her to live a happy life.
Without the random accident of ending up on the same boat, Jack and Rose would never have met, and Rose would never have felt the need to break free from the life that was stifling her.
Love is pretty important in getting Rose and Jack to come together despite the class divide, but really it's Rose's love of art that does the job. She's ready to walk away from Jack and his impertinence until she sees his drawings.
Obviously, love is a key theme in Titanic. It's Titanic, for Valentine's Day's sake. This movie is a complete romance-fest…but love is both powerful and destructive in the film.
Destructive? Well, yeah. Rose and Jack manage to hurt people and risk their own lives (and end up leaving a perfectly good seat empty in a lifeboat) to be together.
But the positives outweigh the negatives when it comes to l'amour in Titanic. Rose was basically drowning, psychologically speaking, when the film began, to the point where she was contemplating literally drowning herself by jumping off the back of the boat.
Jack stops her, and their resulting love helps sustain Rose through all the danger that accompanies the Titanic's sinking. Cameron isn't subtle about it: Jack and Rose's love basically saves Rose's life…but for Jack it's a different story.
The love story works out great for Rose, but since Jack ends up dead, the overall message is that love can't really conquer all.
It's not all about whether Rose literally drowns. What's key is that Jack's love prevents her from drowning in a metaphorical and psychological way. Jack prevents her from dying, yes, but it's more important that he made her find reasons for living.
Rose begins the movie by telling us that boarding Titanic felt like boarding a slave ship to her. Now, while comparing Rose's feelings of family obligation to the experiences and history of slavery is extreme, to put it nicely (and offensive, if we're being more direct), that line drives home just how trapped she's feeling.
She's ended up on a path she hates but thinks she can't escape—she believes she has to marry Cal to save her mother/herself from financial ruin, but she really doesn't want to.
Her family bonds and her social class place incredible demands on her to do and be just the right "thing," but she's so passionate, outspoken, and artistic that she basically finds it impossible to play nicely with others in her social set. Luckily, Jack, the poor, free-spirited artist, is totally willing to help her break the mold and misbehave.
The fact that Rose gave her name as "Rose Dawson" in New York signaled that she was leaving her old life and family behind.
Jack plays a big part in getting Rose to break free, but it's really watching a little girl get schooled on table manners that pushes Rose over the edge and inspires her to find Jack and make out with him. That's the big moment in which she breaks free.