It seems to me we fill the silence because we're not actually comfortable with ourselves. We don't know how to be alone with our own thoughts, so we can't possibly be with our own thoughts in front of someone else. Or maybe we're using that other person as an excuse; a distraction from having to face the one person we can't deal with - ourself.
I used to feel that way. I would spend so much effort trying to create conversation when meeting new people. I'd even resort to talking about the weather, if necessary. Before going out, I'd actually research random news, just to make sure that I didn't run out of things to talk about.
I thought when I met new people, I should be looking for that person with whom I was always talking and laughing. There would never be a lull in conversation. What I found was that while I was meeting and dating all these people that I couldn't really talk with, I was forced to get to know myself.
Once I knew myself, really knew what it was I wanted and was looking for - I found out the right person isn't necessarily someone with whom I have endless conversation. Turns out, it's someone with whom I can talk about anything, to whom I can say what's on my mind - or with whom I can say nothing at all. We can be quiet, together. We can take a long drive, or hang out in the park, and it's okay if we talk the whole time - and it's ok if don't.