I have recently realised how important this is to me when I'm trying to write a story. My main focus is to create believable characters and convince the viewer that the world those characters live in is possible, tangible and real. I think a character is nothing without it's context, it's actually what makes a certain character come to life. What I'm trying to say is that you will have a solid story if the context, the world you created, can generate people like those living characters you see on the screen. Perhaps "generate" is not the most appropriate word but you get the point.
And I believe that it's through that process that the viewers will become attached to your characters. Only then will we be concerned by the obstacles your characters face. Of course, it's the hardest step, but the most important as far as I'm concerned.
How many times did I write "characters"?! Oh well.