Big-Budget Bonanza

The movie features a shipwreck and other related life-ending events (for example, people jumping from the ship, getting trapped under funnels, or careening down the ship when it tips up vertically), so you won't be surprised to hear that some special effects were involved in the filming.

However, it hardly shows, and Cameron's film (including the effects) look pretty much just as though he filmed the events happening in reality.

Of course, that's in large part due to Cameron's commitment to making use of realistic, large-scale models and sets and non-digital effects. So, for example, when he showed water crashing through the glass dome onto the grand staircase, that was actual water destroying the actual set—which meant Cameron had only one chance to get the shot right (source).

So, that's the kind of thinking (and probably a lot of planning) that allowed Cameron to make his film seem realistic, even with all the digital effects.

It's also the kind of thing that probably contributed to the film running way over budget and making studio execs nervous. But they shouldn't have feared: Titanic was the highest-grossing film ever made until Avatar squashed its box office record a decade later.