A few things spring to my mind:

Immigrants
Travelling across water
Star Trek -> Space travel

There's a theme here of journeying to a new place. Maybe you feel you are travelling to a (symbollic) place in your life? Immigrants are moving to a new land to start a new optimistic life full of possibility and opportunity. Perhaps you are feeling anxiety because you believe you may fail on this journey, as the dream involves the Titanic which sunk?

The movie Titanic is also a romance, so it could be something to do with you wanting to find a girlfriend. Not understanding a cute girl is saying may suggest that you are having trouble understanding and communicating with women.

Does this have any resemblence to your life at the moment?