The Heart of the Ocean is the center of the whole story: Lovett is looking for it, that's why he is interested in Rose's story (she knows about it), and Rose wants to take it back where it belongs, so she comes and tells Lovett her story.

We first see it when Cal gives it to Rose after her suicide attempt. It means that now nothing can come between them, they will get married no matter what happens (well, almost...).

We then see it as Rose shows it to Jack to be drawn by him, and during the drawing scene.

It also appears when Lovejoy puts it into Jack's overcoat (well, that's not really his overcoat) and when Steward Barnes pulls it out of the same pocket during the arrestation scene.

Later, during the sinking, Cal takes it out of the safe to put it into his pocket and, as she stands on the Carpathia, looking up at the Statue of Liberty, Rose pulls it back out of the pocket and stares at it with amazement.

The last once we see it is when old Rose drops it back into the sea.