I've been thinking of an answer since you posted this and I'm still have some difficulties. I think the easiest explanation for me is when I'm reading the story and it evokes emotion in me.
I think the two best examples in written work that I can think of right now are in Mercedes Lackey's books... Magic's Pawn. There is a scene where I cry everytime I read it. The scene is so emotionally powerful, you are just sucked into and feel the soulracking pain that the character feels. Another one is in her book Joust... the young boy tries leaping to his death instead of being dragged back to slavery. You can just feel his pain. There is also a rather cute scene in that one where a massive dragon follows the boy like a puppy and everyone around them are amazed to no end that the dragon would do such a thing. It was a very cute scene. Again, you could visualize the dumbfounded looks on the faces of those people. There are many examples in net work as well, though I won't bring up any.
When I'm writing, I try to connect to the reader and make them feel what the characters feel. I want them to have an emotional stake.
I love the replies so far and I'll probably post again after more thought and discussion here.
Myr