I always thought the explanation was fairly simple. It played to the two main demographics: a sweeping love story for the women, and eye-popping special effects for the men.
Michael Bay tried to ape this a few years later, when he crowbarred a love triangle into Pearl Harbor. The war story might have worked okay with the guys, but nobody seemed to buy the romantic plot, and it made only a third of what Titanic grossed domestically.
Since then, Bay has abandoned all subtlety on both fronts, giving us both pouty, sluttulous Megan Fox and blurry, hyperkinetic robot battles. This combination seems to be working much better for him at the box office.